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Math Help - Multiply 2 Matrices to find ABCD in Matrix B

  1. #1
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    Question Multiply 2 Matrices to find ABCD in Matrix B

    I cannot figure out how to do this problem. The way they show you how to do it on my online math homework software is in a very complicated and drawn out longhand way. I am pretty convinced there is a way to do this on my TI-84 calculator since that is what I have been able to do for all my other problems. So I would greatly appreciate it if someone could show me how.
    --------------------------

    Find values for a,b,c and d that satisfy the following matrix equation.



    Matrix 1

    1 -2
    2 -1

    Matrix 2

    a b
    c d

    Matrix 3

    3 -5
    6 2
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, unreal030!

    You never gave us the equation!

    I'll assume that it is: . \text{(Matrix 1)} \times \text{(Matrix 2)} \:=\:\text{(Matrix 3)}


    Find values for a,b,c,d that satisfy the following matrix equation.

    . . \begin{bmatrix}1 &\text{-}2 \\2 &\text{-}1\end{bmatrix}\cdot\begin{bmatrix}a&b\\c&d\end{bm  atrix} \:=\:\begin{bmatrix}3&\text{-}5\\6&2\end{bmatrix}
    If you know anything about matrices, why do you need a calculator?


    Multiply and we have: . \begin{bmatrix}a-2x & b-2d \\ 2a-c & 2b-d\end{bmatrix} \:=\:\begin{bmatrix}3&\text{-}5\\6&2\end{bmatrix}


    And we have four equations: . \begin{array}{cccc}a-2c\:=\:3 & & b-2d \:=\:\text{-}5 \\ 2a-c \:=\:6 & & 2b-d \:=\:2 \end{array}


    Solve the two systems of equations: . \boxed{\begin{array}{ccccc}a \:=\:3 & & b \:=\:3 \\ c\:=\:0 & & d \:=\:4 \end{array}}

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