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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices1 Mark
Question
Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix :

$\left[\begin{array}{ccc}0 & 4 & 7 \\ -4 & 0 & -3 \\ -7 & 3 & 0\end{array}\right]$

✓

Answer

$\begin{aligned} & \text { Let } A=\left[\begin{array}{ccc}0 & 4 & 7 \\ -4 & 0 & -3 \\ -7 & 3 & 0\end{array}\right] \\ & \therefore A^{\top}=\left[\begin{array}{ccc}0 & -4 & -7 \\ 4 & 0 & 3 \\ 7 & -3 & 0\end{array}\right] \\ & \therefore A^{\top}=-\left[\begin{array}{ccc}0 & 4 & 7 \\ -4 & 0 & -3 \\ -7 & 3 & 0\end{array}\right]\end{aligned}$

$\therefore A^{\top}=-\mathrm{A}$, i.e. $\mathrm{A}=-\mathrm{A}^{\top}$

∴ A is a skew-symmetric matrix.

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