MCQ
The matrix $\left[\begin{array}{ccc}0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{array}\right]$ is a:
- Adiagonal matrix
- Bsymmetric matrix
- ✓skew symmetric matrix
- Dscalar matrix
✓
Answer
Correct option: C.
skew symmetric matrix
(C) Skew symmetric matrix
Explanation: We know that, in a square matrix, if $b_{i j}$, when $i \neq j$ then it is said to be a diagonal matrix. Here, $b_{12}, b_{13} \ldots \neq 0$ so the given matrix is not a diagonal matrix.
$\begin{aligned}\text{Now, } B & =\left[\begin{array}{ccc}0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{array}\right] \\ B^{\prime} & =\left[\begin{array}{ccc}0 & 5 & -8 \\ -5 & 0 & -12 \\ -8 & 12 & 0\end{array}\right] \\ & =-\left[\begin{array}{ccc}0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{array}\right] \\ & =-B\end{aligned}$
So, the given matrix is a skew - symmetric matrix, since we know that in a square matrix $B$, if $B^{\prime}=-B$, then it is called skew-symmetric matrix.
Explanation: We know that, in a square matrix, if $b_{i j}$, when $i \neq j$ then it is said to be a diagonal matrix. Here, $b_{12}, b_{13} \ldots \neq 0$ so the given matrix is not a diagonal matrix.
$\begin{aligned}\text{Now, } B & =\left[\begin{array}{ccc}0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{array}\right] \\ B^{\prime} & =\left[\begin{array}{ccc}0 & 5 & -8 \\ -5 & 0 & -12 \\ -8 & 12 & 0\end{array}\right] \\ & =-\left[\begin{array}{ccc}0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0\end{array}\right] \\ & =-B\end{aligned}$
So, the given matrix is a skew - symmetric matrix, since we know that in a square matrix $B$, if $B^{\prime}=-B$, then it is called skew-symmetric matrix.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The graph of the inequality 2x + 3y > 6 is
If $x < 5,$ then
→→
Time series analysis helps to
Total number of possible matrices of order $3 \times 3$ with each entry 2 or 0 is:
→Assume $X , Y , Z~ W$ and $P$ are matrices of order $2 \times n$, $3 \times k, 2 \times p, n \times 3$ and $p \times k$, respectively. If $n=p$, then the order of the matrix $7 X -5 Z$ is:
→Corner points of the feasible region for an LPP are: (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let z = 4x + 6y the objective function. The minimum value of z occurs at
A coin is tossed 10 times. The probability of getting exactly six heads is
A pipe can fill an empty cistern in 5 hours. A leak develops in the cistern due to which full cistern is emptied in 30 hours. With the leak, the cistern can be filled in
If $A=\left|\begin{array}{ccc}2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3\end{array}\right|$, then $A^{-1}$ exist, if
→