InterviewSolution
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InterviewSolution
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The matrix A=\(\begin{bmatrix}2&9\\2&6\end{bmatrix}\) as a sum of symmetric and skew-symmetric matrix is ______(a) \( \frac{1}{4} \begin{bmatrix}4&11\\11&12\end{bmatrix} – \frac{1}{2} \begin{bmatrix}0&7\\-7&0\end{bmatrix}\)(b) \( \frac{1}{4} \begin{bmatrix}4&11\\11&12\end{bmatrix} + \frac{1}{2} \begin{bmatrix}0&7\\7&0\end{bmatrix}\)(c) \( \frac{1}{2} \begin{bmatrix}4&11\\11&12\end{bmatrix} + \frac{1}{2} \begin{bmatrix}0&7\\-7&0\end{bmatrix}\)(d) \( \frac{1}{2} \begin{bmatrix}4&11\\11&12\end{bmatrix} – \frac{1}{2} \begin{bmatrix}0&7\\-7&0\end{bmatrix}\)I have been asked this question during a job interview.Question is taken from Symmetric and Skew Symmetric Matrices in division Matrices of Mathematics – Class 12 |
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Answer» CORRECT choice is (c) \( \frac{1}{2} \BEGIN{BMATRIX}4&11\\11&12\end{bmatrix} + \frac{1}{2} \begin{bmatrix}0&7\\-7&0\end{bmatrix}\) The best explanation: Given that A=\(\begin{bmatrix}2&9\\2&6\end{bmatrix}\). A’=\(\begin{bmatrix}2&2\\9&6\end{bmatrix}\) ⇒A+A’=\(\begin{bmatrix}2&9\\2&6\end{bmatrix}\)+\(\begin{bmatrix}2&2\\9&6\end{bmatrix}\)=\(\begin{bmatrix}4&11\\11&12\end{bmatrix}\) ⇒A-A’=\(\begin{bmatrix}2&9\\2&6\end{bmatrix}\)–\(\begin{bmatrix}2&2\\9&6\end{bmatrix}\)=\(\begin{bmatrix}0&7\\-7&0\end{bmatrix}\) The given square matrix can be written as ⇒A = \( \frac{1}{2}\) (A+A’) + \( \frac{1}{2}\) (A-A’)=\( \frac{1}{2} \begin{bmatrix}4&11\\11&12\end{bmatrix} + \frac{1}{2} \begin{bmatrix}0&7\\-7&0\end{bmatrix}\). |
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