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Mathematics Question on Matrices

If A'=[−23\12]\begin{bmatrix}-2&3\\\1&2\end{bmatrix}and B=[−10\12]\begin{bmatrix}-1&0\\\1&2\end{bmatrix},then find (A+2B)'

Answer

We know that A=(A')'

so A=[−21\32]\begin{bmatrix}-2&1\\\3&2\end{bmatrix}

so A+2B=[−21\32]\begin{bmatrix}-2&1\\\3&2\end{bmatrix}+2[−10\12]\begin{bmatrix}-1&0\\\1&2\end{bmatrix}

=[−21\32]\begin{bmatrix}-2&1\\\3&2\end{bmatrix}+[−20\24]\begin{bmatrix}-2&0\\\2&4\end{bmatrix}=[−41\56]\begin{bmatrix}-4&1\\\5&6\end{bmatrix}

so (A+2B)'=[−45\16]\begin{bmatrix}-4&5\\\1&6\end{bmatrix}