Evaluate the following:

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

Question

Evaluate the following:
$[\begin{matrix} 1 & 2 & 3 \end{matrix}] [\begin{matrix} 1 & 0 & 2 \\ 2 & 0 & 1 \\ 0 & 1 & 2 \end{matrix}] [\begin{array}{c} 2 \\ 4 \\ 6 \end{array}]$

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Consider

{[\begin{array}{ccc} 1 & 2 & 3 \end{array}]}_{1 \times 3} {[\begin{array}{ccc} 1 & 0 & 2 \\ 2 & 0 & 1 \\ 0 & 1 & 2 \end{array}]}_{3 \times 3}

{[\begin{array}{ccc} 1 & 2 & 3 \end{array}]}_{1 \times 3} {[\begin{array}{ccc} 1 & 0 & 2 \\ 2 & 0 & 1 \\ 0 & 1 & 2 \end{array}]}_{3 \times 3}

= [1 + 4 + 0 0 + 0 + 3 2 + 2 + 6]_1×3

= [5 3 10]_1×3

Again

{[\begin{array}{ccc} 5 & 3 & 10 \end{array}]}_{1 \times 3} {[\begin{array}{c} 2 \\ 4 \\ 6 \end{array}]}_{3 \times 1}

= [10 + 12 + 60]_1×1

= 82