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

Question
Matrices
asked 2020-12-16
Given matrix A and matrix B. Find (if possible) the matrices: (a) AB (b) BA.
A=\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix} , B=\begin{bmatrix}1 & 2 & 3 \end{bmatrix}

Answers (1)

2020-12-17
Step 1
\(A=\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix} , B=\begin{bmatrix}1 & 2 & 3 \end{bmatrix}\)
order of \(A = 3 \times 1\)
order of \(B = 1 \times 3\)
Step 2
a)AB
It is possible and order will be 3 \times 3\)
\(\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix}\begin{bmatrix}1 & 2 & 3 \end{bmatrix}=\begin{bmatrix}-1 & -2&-3 \\-2& -4&-6\\-3&-6&-9 \end{bmatrix}\)
Step 3
b)BA
It is possible and order will be \(1 \times 1\)
\(\begin{bmatrix}1 & 2 & 3 \end{bmatrix}\begin{bmatrix}-1 \\-2\\-3 \end{bmatrix}\)
\(=\begin{bmatrix}-1 & -4 & -9 \end{bmatrix}\)
\(=\begin{bmatrix}-14 \end{bmatrix}\)
0

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