Which of the following statements about linear system equations are correct?
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Question: Which of the following statements about linear system equations are correct?
Statements:
A non-homogeneous system equations $Ax = b$ with $A$ of size $6times7$ can have a unique solution for a particular right-hand side $b$.
A homogeneous system equations $Ax = 0$ with the size $6times6$ matrix $A$ can have the amount of all solutions spanned by two vectors.
A non-homogeneous system equations $Ax = b$ with the size $A$ of size $7times6$ can have a unique solution for a particular right-hand side $b$.
A system equations $Ax = 0$ with the size $A$ of size $10times12$ of can have the amount of all solutions consisting of multiples of a vector.
A system equations $Ax = 0$ with the size $7times10$ matrix $A$ can have the amount of all solutions spanned by two vectors.
My answer:
It stands still in my head and I don't know where to start from to be able control of which statement that is true or false. Please help me!
matrices systems-of-equations matrix-equations matrix-calculus
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
asked Dec 19 '18 at 16:34
andersanders
64
$endgroup$
add a comment |
$begingroup$
Question: Which of the following statements about linear system equations are correct?
Statements:
A non-homogeneous system equations $Ax = b$ with $A$ of size $6times7$ can have a unique solution for a particular right-hand side $b$.
A homogeneous system equations $Ax = 0$ with the size $6times6$ matrix $A$ can have the amount of all solutions spanned by two vectors.
A non-homogeneous system equations $Ax = b$ with the size $A$ of size $7times6$ can have a unique solution for a particular right-hand side $b$.
A system equations $Ax = 0$ with the size $A$ of size $10times12$ of can have the amount of all solutions consisting of multiples of a vector.
A system equations $Ax = 0$ with the size $7times10$ matrix $A$ can have the amount of all solutions spanned by two vectors.
My answer:
It stands still in my head and I don't know where to start from to be able control of which statement that is true or false. Please help me!
matrices systems-of-equations matrix-equations matrix-calculus
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
asked Dec 19 '18 at 16:34
andersanders
64
$endgroup$
$begingroup$
Welcome to MSE. We usually don't provide full answers to homework-type questions. I suggest that you provide some thought about your progress so far and the specific points you got stuck. We can give a better feedback this way if we know what exactly is your problem.
$endgroup$
– BigbearZzz
Dec 19 '18 at 16:57
$begingroup$
aha okey i will try to give a better answer
$endgroup$
– anders
Dec 19 '18 at 16:58
add a comment |
$begingroup$
Question: Which of the following statements about linear system equations are correct?
Statements:
A non-homogeneous system equations $Ax = b$ with $A$ of size $6times7$ can have a unique solution for a particular right-hand side $b$.
A homogeneous system equations $Ax = 0$ with the size $6times6$ matrix $A$ can have the amount of all solutions spanned by two vectors.
A non-homogeneous system equations $Ax = b$ with the size $A$ of size $7times6$ can have a unique solution for a particular right-hand side $b$.
A system equations $Ax = 0$ with the size $A$ of size $10times12$ of can have the amount of all solutions consisting of multiples of a vector.
A system equations $Ax = 0$ with the size $7times10$ matrix $A$ can have the amount of all solutions spanned by two vectors.
My answer:
It stands still in my head and I don't know where to start from to be able control of which statement that is true or false. Please help me!
matrices systems-of-equations matrix-equations matrix-calculus
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
asked Dec 19 '18 at 16:34
andersanders
64
$endgroup$
Question: Which of the following statements about linear system equations are correct?
Statements:
A non-homogeneous system equations $Ax = b$ with $A$ of size $6times7$ can have a unique solution for a particular right-hand side $b$.
A homogeneous system equations $Ax = 0$ with the size $6times6$ matrix $A$ can have the amount of all solutions spanned by two vectors.
A non-homogeneous system equations $Ax = b$ with the size $A$ of size $7times6$ can have a unique solution for a particular right-hand side $b$.
A system equations $Ax = 0$ with the size $A$ of size $10times12$ of can have the amount of all solutions consisting of multiples of a vector.
A system equations $Ax = 0$ with the size $7times10$ matrix $A$ can have the amount of all solutions spanned by two vectors.
My answer:
It stands still in my head and I don't know where to start from to be able control of which statement that is true or false. Please help me!
matrices systems-of-equations matrix-equations matrix-calculus
matrices systems-of-equations matrix-equations matrix-calculus
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
asked Dec 19 '18 at 16:34
andersanders
64
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
asked Dec 19 '18 at 16:34
andersanders
64
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
edited Dec 19 '18 at 16:49
Shubham Johri
5,017717
5,017717
asked Dec 19 '18 at 16:34
andersanders
64
asked Dec 19 '18 at 16:34
andersanders
64
asked Dec 19 '18 at 16:34
andersanders
64
64
$begingroup$
Welcome to MSE. We usually don't provide full answers to homework-type questions. I suggest that you provide some thought about your progress so far and the specific points you got stuck. We can give a better feedback this way if we know what exactly is your problem.
$endgroup$
– BigbearZzz
Dec 19 '18 at 16:57
$begingroup$
aha okey i will try to give a better answer
$endgroup$
– anders
Dec 19 '18 at 16:58
add a comment |
$begingroup$
Welcome to MSE. We usually don't provide full answers to homework-type questions. I suggest that you provide some thought about your progress so far and the specific points you got stuck. We can give a better feedback this way if we know what exactly is your problem.
$endgroup$
– BigbearZzz
Dec 19 '18 at 16:57
$begingroup$
aha okey i will try to give a better answer
$endgroup$
– anders
Dec 19 '18 at 16:58
$begingroup$
Welcome to MSE. We usually don't provide full answers to homework-type questions. I suggest that you provide some thought about your progress so far and the specific points you got stuck. We can give a better feedback this way if we know what exactly is your problem.
$endgroup$
– BigbearZzz
Dec 19 '18 at 16:57
$begingroup$
Welcome to MSE. We usually don't provide full answers to homework-type questions. I suggest that you provide some thought about your progress so far and the specific points you got stuck. We can give a better feedback this way if we know what exactly is your problem.
$endgroup$
– BigbearZzz
Dec 19 '18 at 16:57
$begingroup$
aha okey i will try to give a better answer
$endgroup$
– anders
Dec 19 '18 at 16:58
$begingroup$
aha okey i will try to give a better answer
$endgroup$
– anders
Dec 19 '18 at 16:58
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
We can look at it one at a time. I won't just give the answer because it is clearly a homework question but we can work through this together. The first thing you should ask yourself is: What is this question really asking about?
Answer 1 shows an equation Ax=band asks if A is a 6x7 matrix, can we solve for x. Well, what does a 6x7 matrix mean? How many rows and how many columns? What do the columns mean? Notice there is a mismatch between rows and columns, what does that mean?
Answer 2 is like answer one but b = 0, which means what? What does it mean to have a system spanned by vectors?
Answer 3 is like answer 1 but what is different?
Answer 4 is similar to answers 1 and 3 but what is it asking about this time with "multiples of a vector"?
Answer 5 is like answer 2 but what is different?
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
$endgroup$
$begingroup$
1 is a mn matrix but says that is has a unique solution but 3 is also a mn matrix but says that is can have the amount of all solutions spanned by two vectors. 2 is a nn matrix and can have the amount of all solutions spanned by two vectors and 5 is a mn and can have the amount of all solutions spanned by two vectors.
$endgroup$
– anders
Dec 19 '18 at 19:16
$begingroup$
So can answer 1 be true? Can a mn matrix where m < n have a unique solution?
$endgroup$
– Jesse Feng
Dec 19 '18 at 19:19
$begingroup$
I guess that when it is a mn matrix it can have the amount of all solutions spanned by two vectors. When it is a nn it can only have one solution. That gives us that the only ones that are true are 4 and 5. Am I wrong?
$endgroup$
– anders
Dec 19 '18 at 19:20
$begingroup$
Am I thinking correctly?
$endgroup$
– anders
Dec 19 '18 at 19:24
$begingroup$
Please answer me
$endgroup$
– anders
Dec 19 '18 at 19:47
|
show 4 more comments
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
We can look at it one at a time. I won't just give the answer because it is clearly a homework question but we can work through this together. The first thing you should ask yourself is: What is this question really asking about?
Answer 1 shows an equation Ax=band asks if A is a 6x7 matrix, can we solve for x. Well, what does a 6x7 matrix mean? How many rows and how many columns? What do the columns mean? Notice there is a mismatch between rows and columns, what does that mean?
Answer 2 is like answer one but b = 0, which means what? What does it mean to have a system spanned by vectors?
Answer 3 is like answer 1 but what is different?
Answer 4 is similar to answers 1 and 3 but what is it asking about this time with "multiples of a vector"?
Answer 5 is like answer 2 but what is different?
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
$endgroup$
$begingroup$
1 is a mn matrix but says that is has a unique solution but 3 is also a mn matrix but says that is can have the amount of all solutions spanned by two vectors. 2 is a nn matrix and can have the amount of all solutions spanned by two vectors and 5 is a mn and can have the amount of all solutions spanned by two vectors.
$endgroup$
– anders
Dec 19 '18 at 19:16
$begingroup$
So can answer 1 be true? Can a mn matrix where m < n have a unique solution?
$endgroup$
– Jesse Feng
Dec 19 '18 at 19:19
$begingroup$
I guess that when it is a mn matrix it can have the amount of all solutions spanned by two vectors. When it is a nn it can only have one solution. That gives us that the only ones that are true are 4 and 5. Am I wrong?
$endgroup$
– anders
Dec 19 '18 at 19:20
$begingroup$
Am I thinking correctly?
$endgroup$
– anders
Dec 19 '18 at 19:24
$begingroup$
Please answer me
$endgroup$
– anders
Dec 19 '18 at 19:47
|
show 4 more comments
$begingroup$
We can look at it one at a time. I won't just give the answer because it is clearly a homework question but we can work through this together. The first thing you should ask yourself is: What is this question really asking about?
Answer 1 shows an equation Ax=band asks if A is a 6x7 matrix, can we solve for x. Well, what does a 6x7 matrix mean? How many rows and how many columns? What do the columns mean? Notice there is a mismatch between rows and columns, what does that mean?
Answer 2 is like answer one but b = 0, which means what? What does it mean to have a system spanned by vectors?
Answer 3 is like answer 1 but what is different?
Answer 4 is similar to answers 1 and 3 but what is it asking about this time with "multiples of a vector"?
Answer 5 is like answer 2 but what is different?
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
$endgroup$
$begingroup$
1 is a mn matrix but says that is has a unique solution but 3 is also a mn matrix but says that is can have the amount of all solutions spanned by two vectors. 2 is a nn matrix and can have the amount of all solutions spanned by two vectors and 5 is a mn and can have the amount of all solutions spanned by two vectors.
$endgroup$
– anders
Dec 19 '18 at 19:16
$begingroup$
So can answer 1 be true? Can a mn matrix where m < n have a unique solution?
$endgroup$
– Jesse Feng
Dec 19 '18 at 19:19
$begingroup$
I guess that when it is a mn matrix it can have the amount of all solutions spanned by two vectors. When it is a nn it can only have one solution. That gives us that the only ones that are true are 4 and 5. Am I wrong?
$endgroup$
– anders
Dec 19 '18 at 19:20
$begingroup$
Am I thinking correctly?
$endgroup$
– anders
Dec 19 '18 at 19:24
$begingroup$
Please answer me
$endgroup$
– anders
Dec 19 '18 at 19:47
|
show 4 more comments
$begingroup$
We can look at it one at a time. I won't just give the answer because it is clearly a homework question but we can work through this together. The first thing you should ask yourself is: What is this question really asking about?
Answer 1 shows an equation Ax=band asks if A is a 6x7 matrix, can we solve for x. Well, what does a 6x7 matrix mean? How many rows and how many columns? What do the columns mean? Notice there is a mismatch between rows and columns, what does that mean?
Answer 2 is like answer one but b = 0, which means what? What does it mean to have a system spanned by vectors?
Answer 3 is like answer 1 but what is different?
Answer 4 is similar to answers 1 and 3 but what is it asking about this time with "multiples of a vector"?
Answer 5 is like answer 2 but what is different?
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
$endgroup$
We can look at it one at a time. I won't just give the answer because it is clearly a homework question but we can work through this together. The first thing you should ask yourself is: What is this question really asking about?
Answer 1 shows an equation Ax=band asks if A is a 6x7 matrix, can we solve for x. Well, what does a 6x7 matrix mean? How many rows and how many columns? What do the columns mean? Notice there is a mismatch between rows and columns, what does that mean?
Answer 2 is like answer one but b = 0, which means what? What does it mean to have a system spanned by vectors?
Answer 3 is like answer 1 but what is different?
Answer 4 is similar to answers 1 and 3 but what is it asking about this time with "multiples of a vector"?
Answer 5 is like answer 2 but what is different?
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
edited Dec 19 '18 at 19:17
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
answered Dec 19 '18 at 19:11
Jesse FengJesse Feng
12
12
$begingroup$
1 is a mn matrix but says that is has a unique solution but 3 is also a mn matrix but says that is can have the amount of all solutions spanned by two vectors. 2 is a nn matrix and can have the amount of all solutions spanned by two vectors and 5 is a mn and can have the amount of all solutions spanned by two vectors.
$endgroup$
– anders
Dec 19 '18 at 19:16
$begingroup$
So can answer 1 be true? Can a mn matrix where m < n have a unique solution?
$endgroup$
– Jesse Feng
Dec 19 '18 at 19:19
$begingroup$
I guess that when it is a mn matrix it can have the amount of all solutions spanned by two vectors. When it is a nn it can only have one solution. That gives us that the only ones that are true are 4 and 5. Am I wrong?
$endgroup$
– anders
Dec 19 '18 at 19:20
$begingroup$
Am I thinking correctly?
$endgroup$
– anders
Dec 19 '18 at 19:24
$begingroup$
Please answer me
$endgroup$
– anders
Dec 19 '18 at 19:47
|
show 4 more comments
$begingroup$
1 is a mn matrix but says that is has a unique solution but 3 is also a mn matrix but says that is can have the amount of all solutions spanned by two vectors. 2 is a nn matrix and can have the amount of all solutions spanned by two vectors and 5 is a mn and can have the amount of all solutions spanned by two vectors.
$endgroup$
– anders
Dec 19 '18 at 19:16
$begingroup$
So can answer 1 be true? Can a mn matrix where m < n have a unique solution?
$endgroup$
– Jesse Feng
Dec 19 '18 at 19:19
$begingroup$
I guess that when it is a mn matrix it can have the amount of all solutions spanned by two vectors. When it is a nn it can only have one solution. That gives us that the only ones that are true are 4 and 5. Am I wrong?
$endgroup$
– anders
Dec 19 '18 at 19:20
$begingroup$
Am I thinking correctly?
$endgroup$
– anders
Dec 19 '18 at 19:24
$begingroup$
Please answer me
$endgroup$
– anders
Dec 19 '18 at 19:47
$begingroup$
1 is a mn matrix but says that is has a unique solution but 3 is also a mn matrix but says that is can have the amount of all solutions spanned by two vectors. 2 is a nn matrix and can have the amount of all solutions spanned by two vectors and 5 is a mn and can have the amount of all solutions spanned by two vectors.
$endgroup$
– anders
Dec 19 '18 at 19:16
$begingroup$
1 is a mn matrix but says that is has a unique solution but 3 is also a mn matrix but says that is can have the amount of all solutions spanned by two vectors. 2 is a nn matrix and can have the amount of all solutions spanned by two vectors and 5 is a mn and can have the amount of all solutions spanned by two vectors.
$endgroup$
– anders
Dec 19 '18 at 19:16
$begingroup$
So can answer 1 be true? Can a mn matrix where m < n have a unique solution?
$endgroup$
– Jesse Feng
Dec 19 '18 at 19:19
$begingroup$
So can answer 1 be true? Can a mn matrix where m < n have a unique solution?
$endgroup$
– Jesse Feng
Dec 19 '18 at 19:19
$begingroup$
I guess that when it is a mn matrix it can have the amount of all solutions spanned by two vectors. When it is a nn it can only have one solution. That gives us that the only ones that are true are 4 and 5. Am I wrong?
$endgroup$
– anders
Dec 19 '18 at 19:20
$begingroup$
I guess that when it is a mn matrix it can have the amount of all solutions spanned by two vectors. When it is a nn it can only have one solution. That gives us that the only ones that are true are 4 and 5. Am I wrong?
$endgroup$
– anders
Dec 19 '18 at 19:20
$begingroup$
Am I thinking correctly?
$endgroup$
– anders
Dec 19 '18 at 19:24
$begingroup$
Am I thinking correctly?
$endgroup$
– anders
Dec 19 '18 at 19:24
$begingroup$
Please answer me
$endgroup$
– anders
Dec 19 '18 at 19:47
$begingroup$
Please answer me
$endgroup$
– anders
Dec 19 '18 at 19:47
|
show 4 more comments
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$begingroup$
Welcome to MSE. We usually don't provide full answers to homework-type questions. I suggest that you provide some thought about your progress so far and the specific points you got stuck. We can give a better feedback this way if we know what exactly is your problem.
$endgroup$
– BigbearZzz
Dec 19 '18 at 16:57
$begingroup$
aha okey i will try to give a better answer
$endgroup$
– anders
Dec 19 '18 at 16:58