Choose the correct answer from the given four options. The matrix…

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

The value of the integral $\int \limits_{0}^{1} \frac{\sqrt{x} d x}{(1+x)(1+3 x)(3+x)}$ is:

→

Let $f: R \rightarrow R$ be a continuous function such that $f(x)+f(x+1)=2,$ for all $x \in R$. If $I _{1}=\int_{0}^{8} f( x ) d x$ and $I _{2}=\int_{-1}^{3} f( x ) d x ,$ then the value of $I _{1}+2 I _{2}$ is equal to...........

→

If $A = \left[ {\begin{array}{*{20}{c}}3&2\\1&4\end{array}} \right]$, then $A(adj\,A) = $

→

If $X$ follows a binomial distribution with parameter $\text{n}=8$ and $\text{p}=\frac{1}{2},$ then $\text{P(|X}-4|\leq2)$ equals :

→

Let $f :[ a , b ] \rightarrow[1, \infty)$ be a continuous function and let $g : R \rightarrow R$ be defined as

$g(x)=\left\{\begin{array}{ccc}0 & \text { if } & x < a, \\ \int_a^x f(t) d t & \text { if } & a \leq x \leq b, \\ \int_a^b f(t) d t & \text { if } & x > b .\end{array}\right.$, Then

$(A)$ $g(x)$ is continuous but not differentiable at a

$(B)$ $g(x)$ is differentiable on $R$

$(C)$ $g(x)$ is continuous but not differentiable at $b$

$(D)$ $g(x)$ is continuous and differentiable at either a or $b$ but not both

→

If $\big[2\vec{\text{a}}+4\vec{\text{b}}\vec{\text{c}}\vec{\text{d}}\big]=\lambda\big[\vec{\text{a}}\vec{\text{c}}\vec{\text{d}}\big]+\mu\big[\vec{\text{b}}\vec{\text{c}}\vec{\text{d}}\big],$ then $\lambda+\mu=$

→

A root of the equation $\left| {\,\begin{array}{*{20}{c}}{3 - x}&{ - 6}&3\\{ - 6}&{3 - x}&3\\3&3&{ - 6 - x}\end{array}\,} \right| = 0$ is

→

The construction company uses concrete blocks made up of cement and sand. The weight of a concrete block has to be at least $5 kg$. Cement costs ₹ 20 per kg, while sand costs ₹ 6 per kg. Strength considerations dictate that the concrete block should contain minimum $4 kg$ of cement and not more than $2 kg$ of sand. Formulate the L.P.P for the cost to be minimum.

→

If $\mathrm{a}_{\mathrm{r}}=\cos \frac{2 \mathrm{r} \pi}{9}+i \sin \frac{2 \mathrm{r} \pi}{9}, \mathrm{r}=1,2,3, \ldots, i=\sqrt{-1}$ then the determinant $\left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right|$ is equal to :