If and then find B

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If $3 A - 2 B = (\begin{array}{cc} 1 & - 2 \\ 3 & 0 \end{array})$ and $2 A - 3 B = (\begin{array}{cc} - 3 & 3 \\ 1 & - 1 \end{array})$ then find B

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3 A - 2 B = (\begin{array}{cc} 1 & - 2 \\ 3 & 0 \end{array})

2 A - 3 B = (\begin{array}{cc} - 3 & 3 \\ 1 & - 1 \end{array})

2(3A – 2B) – 3(2A – 3B) = 6A – 4B – 6A + 9B

5 B = 2 (\begin{array}{cc} 1 & - 2 \\ 3 & 0 \end{array}) - 3 (\begin{array}{cc} - 3 & 3 \\ 1 & - 1 \end{array})

5 B = (\begin{array}{cc} 2 & - 4 \\ 6 & 0 \end{array}) - (\begin{array}{cc} - 9 & 9 \\ 3 & - 3 \end{array})

5 B = (\begin{array}{cc} 2 - 9 & - 4 - 9 \\ 6 - 3 & 0 + 3 \end{array})

5 B = (\begin{array}{cc} - 7 & - 13 \\ 3 & 3 \end{array})

B = \frac{1}{5} (\begin{array}{cc} - 7 & - 13 \\ 3 & 3 \end{array})

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