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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES5 Marks
Question
If the matrix $\begin{bmatrix}0&\text{a}&3\\2&\text{b}&-1\\\text{c}&1&0\end{bmatrix}$ is a skew-symmetric matrix, then find the values of a, b and c.
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Answer

Let $\text{A}=\begin{bmatrix}0&\text{a}&3\\2&\text{b}&-1\\\text{c}&1&0\end{bmatrix}$ Since, A is skew-symmetric matrix. $\therefore\ \text{A}'=-\text{A}$$\Rightarrow\ \begin{bmatrix}0&2&\text{c}\\\text{a}&\text{b}&1\\3&-1&0\end{bmatrix}=\begin{bmatrix}0&\text{a}&3\\2&\text{b}&-1\\\text{c}&1&0\end{bmatrix}$
$\Rightarrow\ \begin{bmatrix}0&2&\text{c}\\\text{a}&\text{b}&1\\3&-1&0\end{bmatrix}=\begin{bmatrix}0&-\text{a}&-3\\-2&-\text{b}&1\\-\text{c}&-1&0\end{bmatrix}$ By equality of matrices, we get a = -2, c = -3 and b = -b ⇒ b = 0 $\therefore$ a = -2, b = 0 and c = -3

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