If and is the product AB possible ? Give a reason. If yes find AB.

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $A = [\begin{array}{cc} 3 & 5 \\ 4 & - 2 \end{array}]$ and $B = [\begin{array}{l} 2 \\ 4 \end{array}]$ is the product AB possible ? Give a reason. If yes find AB.

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Yes, the product is possible because of the number of column in A = number of row in B
That is the order of the matrix is 2 × 1
$AB = [\begin{array}{cc} 3 & 5 \\ 4 & - 2 \end{array}] [\begin{array}{l} 2 \\ 4 \end{array}] = [\begin{array}{c} 3 \times 2 + 5 \times 4 \\ 4 \times 2 + (- 2) \times 4 \end{array}]$

$= [\begin{array}{c} 6 + 20 \\ 8 - 8 \end{array}] = [\begin{array}{c} 26 \\ 0 \end{array}]$