# [SOLVED] Matrix multiplication

• February 7th 2010, 01:17 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
• February 7th 2010, 01:27 AM
math2009
$
\begin{bmatrix}
7 &-4 \\
3 &-1 \\
\end{bmatrix}
\begin{bmatrix}
x &y \\
z &w \\
\end{bmatrix}
=\begin{bmatrix}
1 &0 \\
0 &1 \\
\end{bmatrix}

$

$
\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}

$
• February 7th 2010, 02:50 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.
• February 7th 2010, 11:39 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