# Thread: Multiply 2 Matrices to find ABCD in Matrix B

1. ## 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.
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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

2. 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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# find a b c d so tha

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