Question

Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA. A=begin{bmatrix}3 & -2 1 & 5end{bmatrix} , B=begin{bmatrix}0 & 0 5 & -6 end{bmatrix}

Matrices
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asked 2021-03-02
Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.
\(A=\begin{bmatrix}3 & -2 \\1 & 5\end{bmatrix} , B=\begin{bmatrix}0 & 0 \\5 & -6 \end{bmatrix}\)

Answers (1)

2021-03-03
Step 1
Given: \(A=\begin{bmatrix}3 & -2 \\1 & 5\end{bmatrix}_{2 \times 2} , B=\begin{bmatrix}0 & 0 \\5 & -6 \end{bmatrix}_{2 \times 2}\)
Step 2 \(AB=\begin{bmatrix}3 & -2 \\1 & 5\end{bmatrix}\begin{bmatrix}0 & 0 \\5 & -6 \end{bmatrix}\)
\(=\begin{bmatrix}3\times0-2\times5 & 3\times0+2\times6 \\1\times0+5\times5 & 1\times0-6\times5 \end{bmatrix}\)
\(=\begin{bmatrix}0-10 & 0+12 \\0+25 & 0-30 \end{bmatrix}=\begin{bmatrix}-10 & 12 \\25 & -30 \end{bmatrix}\)
\(BA=\begin{bmatrix}0 & 0 \\5 & -6 \end{bmatrix}\begin{bmatrix}3 & -2 \\1 & 5\end{bmatrix}=\begin{bmatrix}0\times3+0\times1 & 0\times(-2)+0\times5 \\5\times3-6\times1 & 5\times(-1)-6\times5 \end{bmatrix}\)
\(=\begin{bmatrix}0+1 & 0 \\15-6 & -10-30 \end{bmatrix}=\begin{bmatrix}1 & 0 \\9 & -40 \end{bmatrix}\)
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