If and then find A + BT.

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If $A = [\begin{array}{ccc} 2 & 3 & - 4 \\ - 1 & 2 & 3 \end{array}]$ and $B = [\begin{array}{cc} - 1 & 2 \\ 3 & 4 \\ - 5 & - 6 \end{array}]$ then find A + B^T.

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Given, $A = [\begin{array}{ccc} 2 & 3 & - 4 \\ - 1 & 2 & 3 \end{array}], B = [\begin{array}{cc} - 1 & 2 \\ 3 & 4 \\ - 5 & - 6 \end{array}]$

∴ B^{T} = [\begin{array}{ccc} - 1 & 3 & - 5 \\ 2 & 4 & - 6 \end{array}]

∴ A + B^{T} = [\begin{array}{ccc} 2 & 3 & - 4 \\ - 1 & 2 & 3 \end{array}] + [\begin{array}{ccc} - 1 & 3 & - 5 \\ 2 & 4 & - 6 \end{array}]

= [\begin{array}{ccc} 2 + (- 1) & 3 + 3 & - 4 + (- 5) \\ - 1 + 2 & 2 + 4 & 3 + (- 6) \end{array}]

= [\begin{array}{ccc} 1 & 6 & - 9 \\ 1 & 6 & - 3 \end{array}]

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