# Thread: Quick Question regarding Matrices.

1. ## Quick Question regarding Matrices.

Inverting and solving equations

Code:
1  -2  1
3  1  2
-1  4  1
Find the inverse of that matrix, hence solve the following

x-2y+z=1

I have 2 more equations to solve, but I just need a quick rundown of the process

To invert, I found the determinant (answer for it was -4 if anyone could confirm to see if I did the method right)

I then took the transpose, and prcoeeded to complete that big 3x3 thing which involves taking the multiplication of diagonal "\" and add it to the multiplication of diagonal "/".

The result of both the transpose and that process gave me this answer:

Code:
9 -6   5
-1  0  -5
11  -2  7
What made me doubt everything was that the 3 equations given simply don't match up with either the inverse of the provided matrix, with the matrix itself, or anything similar that I can recall.

Any help on this would be much appreciated.

2. Originally Posted by Lonehwolf
Inverting and solving equations

Code:
1  -2  1
3  1  2
-1  4  1
Find the inverse of that matrix, hence solve the following

x-2y+z=1

I have 2 more equations to solve, but I just need a quick rundown of the process

To invert, I found the determinant (answer for it was -4 if anyone could confirm to see if I did the method right)

I then took the transpose, and prcoeeded to complete that big 3x3 thing which involves taking the multiplication of diagonal "\" and add it to the multiplication of diagonal "/".

The result of both the transpose and that process gave me this answer:

Code:
9 -6   5
-1  0  -5
11  -2  7
What made me doubt everything was that the 3 equations given simply don't match up with either the inverse of the provided matrix, with the matrix itself, or anything similar that I can recall.

Any help on this would be much appreciated.
Actually the one equation you do happen to give does match with the given coeffcient matrix, and I'm sure the other two equations do to.

I hope you realise that to solve $AX = B$ you do the following: $A^{-1} A X = A^{-1} B \Rightarrow X = A^{-1} B$.

Your inverse is wrong. And the determinant is 16, not -4.

I rather like the method for finding the inverse that is explained so well here: Matrix Inversion: Finding the Inverse of a Matrix

3. Originally Posted by mr fantastic
Actually the one equation you do happen to give does match with the given coeffcient matrix, and I'm sure the other two equations do to.

I hope you realise that to solve $AX = B$ you do the following: $A^{-1} A X = A^{-1} B \Rightarrow X = A^{-1} B$.

Your inverse is wrong. And the determinant is 16, not -4.

I rather like the method for finding the inverse that is explained so well here: Matrix Inversion: Finding the Inverse of a Matrix

Thanks, go the determinant right finally.

Regarding matching the equation with the coefficient matrix - I can't figure that one out. Which line has specifically matched?

Reworking the transpose and that big square thingy I ended up with a different result:
Code:
9 -2  -3
-1 0  -5
11 -6 -5

4. Originally Posted by Lonehwolf
Thanks, go the determinant right finally.

Regarding matching the equation with the coefficient matrix - I can't figure that one out. Which line has specifically matched?

Reworking the transpose and that big square thingy I ended up with a different result:
Code:
9 -2  -3
-1 0  -5
11 -6 -5
Look at the coeeficients of the first equation and look at the first line of your coefficient matrix ....

Your inverse is still wrong. You only have to multiply the two matrices together to quickly see this ....