Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES1 Mark
MCQ
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:
  • A
    Diagonal matrix.
  • B
    Symmetric matrix.
  • ✓
    Skew-symmetric matrix.
  • D
    Scalar matrix.
✓

Answer

Correct option: C.
Skew-symmetric matrix.
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 $f(x) = {x^{11}} + {\sin ^3}\left( {35x} \right) + 111x$ , then the value of ${f^{ - 1}}\left( {\sin \frac{\pi }{5}} \right) + {f^{ - 1}}\left( {\sin \frac{{6\pi }}{5}} \right) + {f^{ - 1}}\left( {\sin \frac{\pi }{7}} \right) + {f^{ - 1}}\left( {\sin \frac{{8\pi }}{7}} \right)$ is equal to
→
Let $\Delta$ be the area of the region $\left\{( x , y ) \in R ^2: x ^2+ y ^2 \leq 21, y ^2 \leq 4 x , x \geq 1\right\}$. Then $\frac{1}{2}\left(\Delta-21 \sin ^{-1} \frac{2}{\sqrt{7}}\right)$ is equal to
→
From a set of 100 cards numbered 1 to 100, one card is drawn at randow. The probability number obtained on the card is divisible by 6 or 8 but not by 24 is
→
In solving the LPP: “minimize f = 6x + 10y subect to constraints $\text{x}\geq6,\text{y}\geq2,2\text{x}+\text{y}\geq10,\text{x}\geq0,\text{y}\geq0$” redundant constraints are:
→
If $f(x)$ and $g(x)$ are two polynomials such that the polynomial $P ( x )=f\left( x ^{3}\right)+ xg \left( x ^{3}\right)$ is divisible by $x^{2}+x+1,$ then $P(1)$ is equal to ....... .
→
Let $f(x)$ be a polynomial of degree $3$ such that $f(3)=1$, $f'(3) =  -1$, $f''(3) = 0$ and $f'''(3)=12$ . Then the value of $f'(1)$is
→
If ${\Delta _1} = \left| {\,\begin{array}{*{20}{c}}x&b&b\\a&x&b\\a&a&x\end{array}\,} \right|$ and ${\Delta _2} = \left| {\,\begin{array}{*{20}{c}}x&b\\a&x\end{array}\,} \right|$ are the given determinants, then
→
If $\left[ {\begin{array}{*{20}{c}}{x + y}&{2x + z}\\{x - y}&{2z + w}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}4&7\\0&{10}\end{array}} \right]$, then values of $x, y, z, w$ are
→
Differential equation having solution $y=A x+B^3$ is of order
→
Let $n \geq 2$ be a natural number and $f:[0,1] \rightarrow R$ be the function defined by

$f(x)= \begin{cases}n(1-2 n x)  \text { if } 0 \leq x \leq \frac{1}{2 n}2 n(2 n x-1)  \text { if } \frac{1}{2 n} \leq x \leq \frac{3}{4 n}4 n(1-n x)  \text { if } \frac{3}{4 n} \leq x \leq \frac{1}{n} \\ \frac{n}{n-1}(n x-1)  \text { if } \frac{1}{n} \leq x \leq 1\end{cases}$

If $n$ is such that the area of the region bounded by the curves $x=0, x=1, y=0$ and $y=f(x)$ is $4$ , then the maximum value of the function $f$ is

→