How would I solve the following using matrices?

sktsasus

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Sep 17, 2017
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1) -2x+5y-9z=0
I am supposed to give the answer in the following form:
The first matrix is regular, the second one will be a product of s, and the third one will be a product of t. Each matrix has 3 numbers in it.

2) -2x1+x2=3
8x1-4x2=-12
The answer is supposed to be in the form:
First matrix is regular, second matrix is a product of s. Each matrix has two numbers in it.

3) 5x1-4x2+4x3+3x4=3
-x1+x2+3x3+3x4=5
4x1-3x2+7x3+6x4=8
3x1-3x2-9x3-9x4=-15
The answer is supposed to be in the form:
First matrix is regular, second matrix is a product of s, third matrix is a product of t. Each matrix has 4 numbers in it.

I know how to find the original matrices for all of these. But I am not sure how to compute them into the forms above. Would I have to carry out elementary operations and convert them into row-echelon form? If so, then what?

4) x + y + 2z=-1
x + 2y -5z= 0
8x + 17y + kz= 2
I am supposed to figure out for what value of k the system has no solutions. I tried to convert the matrix into row-echelon form (with the aim that the bottom row would have 2 zeros) and ended up getting k values of either 8 and/or 17. Both were incorrect.

5) The following is a matrix:
4 -6 2 -6
-2 3 -1 3
I am supposed to find a set of basic solutions for the homogeneous system AX=0

This last one I am not sure how to do at all.

Any help would be highly appreciated.
 
Last edited:
Well, let's see your work. We would love to assist you in your efforts.

Hint? Change he variable list into a column vector. This might be a hint, but I really can't tell where you are stuck.
 
1) -2x+5y-9z=0
I am supposed to give the answer in the following form:
The first matrix is regular, the second one will be a product of s, and the third one will be a product of t. Each matrix has 3 numbers in it.

2) -2x1+x2=3
8x1-4x2=-12
The answer is supposed to be in the form:
First matrix is regular, second matrix is a product of s. Each matrix has two numbers in it.

3) 5x1-4x2+4x3+3x4=3
-x1+x2+3x3+3x4=5
4x1-3x2+7x3+6x4=8
3x1-3x2-9x3-9x4=-15
The answer is supposed to be in the form:
First matrix is regular, second matrix is a product of s, third matrix is a product of t. Each matrix has 4 numbers in it.

I know how to find the original matrices for all of these. But I am not sure how to compute them into the forms above. Would I have to carry out elementary operations and convert them into row-echelon form? If so, then what?

4) x + y + 2z=-1
x + 2y -5z= 0
8x + 17y + kz= 2
I am supposed to figure out for what value of k the system has no solutions. I tried to convert the matrix into row-echelon form (with the aim that the bottom row would have 2 zeros) and ended up getting k values of either 8 and/or 17. Both were incorrect.

5) The following is a matrix:
4 -6 2 -6
-2 3 -1 3
I am supposed to find a set of basic solutions for the homogeneous system AX=0

This last one I am not sure how to do at all.

Any help would be highly appreciated.
Have you studied matrix inversion?
 
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