Compute the product AB and BA whichever exists in the following case:A = [1

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

Question

Compute the product AB and BA whichever exists in the following case:
A = [1 – 1 2 3] and $B = [\begin{array}{c} 0 \\ 1 \\ 3 \\ 2 \end{array}]$

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A = [1 –1 2 3] and $B = [\begin{array}{c} 0 \\ 1 \\ 3 \\ 2 \end{array}]$

⇒ AB = [1 – 1 2 3] $[\begin{array}{c} 0 \\ 1 \\ 3 \\ 2 \end{array}]$

= [0 + (–1) + 6 + 6]

= [11]

∴ AB = [11]

\Rightarrow BA = [\begin{array}{c} 0 \\ 1 \\ 3 \\ 2 \end{array}] [\begin{array}{cccc} 1 & - 1 & 2 & 3 \end{array}]

= [\begin{array}{cccc} 0 & 0 & 0 & 0 \\ 1 & - 1 & 2 & 3 \\ 3 & - 3 & 6 & 9 \\ 2 & - 2 & 4 & 6 \end{array}]

∴ BA = [\begin{array}{cccc} 0 & 0 & 0 & 0 \\ 1 & - 1 & 2 & 3 \\ 3 & - 3 & 6 & 9 \\ 2 & - 2 & 4 & 6 \end{array}]