Perform the multiplication of the matrices ,

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

Question

Perform the multiplication of the matrices $A = [\begin{array}{cc} 3 & 2 \\ 2 & 1 \\ 5 & 4 \end{array}]$ , $B = [\begin{array}{cc} 2 & 4 \\ 5 & 3 \end{array}]$

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$AB = [\begin{array}{ll} 3 2 \\ 2 1 \\ 5 4 \end{array}] [\begin{array}{ll} 2 4 \\ 5 3 \end{array}]$

$= [\begin{array}{cc} 3 \times 2 + 2 \times 5 & 3 \times 4 + 2 \times 3 \\ 4 + 5 & 8 + 3 \\ 10 + 20 & 20 + 12 \end{array}]$

$= [\begin{array}{cc} 16 & 18 \\ 9 & 11 \\ 30 & 32 \end{array}]$