# [SOLVED] Matrix multiplication

• Feb 7th 2010, 12:17 AM
Juggalomike
[SOLVED] Matrix multiplication
I am not sure what i am doing wrong in this question

Q. find a 2x2 matrix such that

|7 -4| |x y| |1 0|
|3 -1| * |z w|= |0 1|

I set it up like this

7x-4z=1
7y-4w=0
3x-1z=0
3y-1w=1

but whenever i solve for x and y i get an incorrect answer, not sure what i am doing wrong
• Feb 7th 2010, 12:27 AM
math2009
$\displaystyle \begin{bmatrix} 7 &-4 \\ 3 &-1 \\ \end{bmatrix} \begin{bmatrix} x &y \\ z &w \\ \end{bmatrix} =\begin{bmatrix} 1 &0 \\ 0 &1 \\ \end{bmatrix}$

$\displaystyle \begin{bmatrix} x &y \\ z &w \\ \end{bmatrix} =\begin{bmatrix} 7 &-4 \\ 3 &-1 \\ \end{bmatrix}^{-1} \begin{bmatrix} 1 &0 \\ 0 &1 \\ \end{bmatrix} =\begin{bmatrix} 7 &-4 \\ 3 &-1 \\ \end{bmatrix}^{-1} =\frac{1}{5} \begin{bmatrix} -1 &4 \\ -3 &7 \\ \end{bmatrix}$
• Feb 7th 2010, 01:50 AM
HallsofIvy
Quote:

Originally Posted by Juggalomike
I am not sure what i am doing wrong in this question

Q. find a 2x2 matrix such that

|7 -4| |x y| |1 0|
|3 -1| * |z w|= |0 1|

I set it up like this

7x-4z=1
7y-4w=0
3x-1z=0
3y-1w=1

but whenever i solve for x and y i get an incorrect answer, not sure what i am doing wrong

We can't tell you what you have done wrong if you don't tell us what you did! What you have so far is perfectly valid.

7x- 4z= 1 and 3x- z= 0 so 12x- 4z= 0 and subtracting one equation from the other, 7x- 12x= -5x= 1 so x= -1/5.

Then 3x- z= -3/5- z= 0 so z= -3/5.

7y- 4w= 0 and 3y- w= 1 so 12y- 4w= 4. Subtracting, 7y- 12y= -5y= -4 so y= 4/5. Then 3y- w= 12/5- w= 1 so w= 12/5- 5/5= 7/5.

That's exactly the same answer as math2009 got.
• Feb 7th 2010, 10:39 AM
Juggalomike
ah ok i see what i was doing wrong lol, yeh sorry, should have probably posted my work after making the equations, was thinking my error was in the making of the equations not solving them