If and , then find AB

Engineering

Mathematics

Algebra of Matrices

Question

If $A = [\begin{array}{cc} 1 & 2 \\ - 3 & 4 \end{array}]$ and $B = [\begin{array}{c} 5 \\ - 1 \end{array}]$ , then find AB

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Given $A = [\begin{array}{cc} 1 & 2 \\ - 3 & 4 \end{array}]$ and $B = [\begin{array}{c} 5 \\ - 1 \end{array}]$ ,

AB = [\begin{array}{cc} 1 & 2 \\ - 3 & 4 \end{array}] [\begin{array}{c} 5 \\ - 1 \end{array}]

[\begin{array}{c} 1 \times 5 + 2 \times 1 \\ - 3 \times 5 + 4 \times - 1 \end{array}]

[\begin{array}{c} 5 - 2 \\ - 15 - 4 \end{array}] = [\begin{array}{c} 3 \\ - 19 \end{array}]