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Math Help - [SOLVED] Matrix multiplication

  1. #1
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    [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
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  2. #2
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    <br />
\begin{bmatrix}<br />
7 &-4 \\<br />
3 &-1 \\<br />
\end{bmatrix}<br />
\begin{bmatrix}<br />
x &y \\<br />
z &w \\<br />
\end{bmatrix}<br />
=\begin{bmatrix}<br />
1 &0 \\<br />
0 &1 \\<br />
\end{bmatrix}<br /> <br />

    <br />
\begin{bmatrix}<br />
x &y \\<br />
z &w \\<br />
\end{bmatrix}<br />
=\begin{bmatrix}<br />
 7 &-4 \\<br />
 3 &-1 \\<br />
 \end{bmatrix}^{-1}<br />
\begin{bmatrix}<br />
1 &0 \\<br />
0 &1 \\<br />
\end{bmatrix}<br />
=\begin{bmatrix}<br />
  7 &-4 \\<br />
  3 &-1 \\<br />
  \end{bmatrix}^{-1}<br />
=\frac{1}{5}<br />
\begin{bmatrix}<br />
  -1 &4 \\<br />
  -3 &7 \\<br />
  \end{bmatrix}<br /> <br />
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  3. #3
    MHF Contributor

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    Quote Originally Posted by Juggalomike View Post
    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.
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  4. #4
    Junior Member
    Joined
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    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
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