Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES1 Mark
Question
Choose the correct answer from the given four options.
The matrix $\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$ is a:
  1. Diagonal matrix.
  2. Symmetric matrix.
  3. Skew-symmetric matrix.
  4. Scalar matrix.
✓

Answer

  1. Skew-symmetric matrix.

Solution:

We have $\text{B}=\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$

$\Rightarrow\ \text{B}'=\begin{bmatrix}0&5&8\\-5&0&-12\\8&12&0\end{bmatrix}$

$=-\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$

$=-\text{B}$

Since, B' = -B,

Thus, B is a 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.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from MATRICES→MATRICES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\int\text{f}(\text{x})\text{dx}=-2\cos\sqrt{\text{x}}+\text{c}$ then f(x) is equal to:
  1. $\sin\sqrt{\text{x}}$
  2. $\frac{\sin\sqrt{\text{x}}}{\sqrt{\text{x}}}$
  3. $2\cos\sqrt{\text{x}}$
  4. None of these 
→
Let $\quad f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{array}\right|$, $x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right]$. If $\alpha$ and $ \beta$ respectively are the maximum and the minimum values of $f$, then
→
In order that the function $f(x) = {(x + 1)^{1/x}}$ is continuous at $x = 0$, $f(0)$ must be defined as
→
Choose the correct answer from the given four options:
The area of the region bounded by the curve $\text{y}=\sqrt{16-\text{x}^2}$ and x-axis is:
  1. $8\text{ sq. units}$
  2. $20\pi\text{ sq. units}$
  3. $16\pi\text{ sq. units}$
  4. $256\pi\text{ sq. units}$
→
In a $\Delta ABC,$ if $\left| {\,\begin{array}{*{20}{c}}1&a&b\\1&c&a\\1&b&c\end{array}\,} \right| = 0$, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C = $
→
If $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&{i/2}\end{array}} \right]$ $(i = \sqrt { - 1} ),$then ${A^{ - 1}}$=
→
The number of solutions of the system of equations:
2x + y − z = 7
x − 3y + 2z = 1
x + 4y − 3z = 5
  1. 3
  2. 2
  3. 1
  4. 0
→
$\int_{}^{} {\frac{{{e^x}dx}}{{\sqrt {a + b{e^x}} }}} = $
→
Choose the correct answer from the given four options.
If A and B are matrices of same order, then (AB′ – BA′) is a:
  1. Skew symmetric matrix.
  2. Null matrix.
  3. Symmetric matrix.
  4. Unit matrix.
→
If the function $f(x) = \left\{ \begin{array}{l}\,\,\,\,\,x + {a^2}\sqrt 2 \sin x,\,0 \le x < \pi /4\\\,\,\,\,\,\,\,\,\,\,\,\,\,x\cot x + b,\,\pi /4 \le x < \pi /2\\b\sin 2x - a\cos 2x,\,\pi /2 \le x \le \pi \end{array} \right.$ is continuous in the interval $[0,\,\pi ]$, then the values of $(a,\,b)$ are
→