Construct a 2 2 matrix A = [a_ ij ] whose elements a_ ij are give… - Vidyadip

Question

Construct a $2 \times 2$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by:$\frac{(\text{i}+\text{j})^2}{2}$

✓

Answer

Here,
$\text{a}_{11}=\frac{(1+1)^2}{2}=\frac{(2)^2}{2}=\frac{4}{2}=2,$ $\text{a}_{12}=\frac{(1+2)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2}$
$\text{a}_{21}=\frac{(2+1)^2}{2}=\frac{(3)^2}{2}=\frac{9}{2},$ $\text{a}_{22}=\frac{(2+2)^2}{2}=\frac{(4)^2}{2}=\frac{16}{2}=8$
So, the required matrix is $\begin{bmatrix}2\frac{9}{2}\\\frac{9}{2}8\end{bmatrix}.$

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 "2 Marks Questions" 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 $|\vec{\text{a}}|=2,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=3,$ find the projection of $\vec{\text{b}}$ on $\vec{\text{a}}.$

Find $\frac{\text{dy}}{\text{dx}},$ when
$x = at^2$ and $y = 2at$

If $\text{A}=\begin{bmatrix}2&1&4\\4&1&5 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}3&-1\\2&2\\1&3\end{bmatrix}.$ Write the order of AB and BA.

A discrete random variable X has the probability distribution given below:

X:	0.5	1	1.5	2
P(X):	k	$k^2$	$2k^2$	k

Find the value of k.

In a competition A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. Find the probability that A losses.

Integrate $\frac{1}{x^2-6 x+13}$ with respect to $x$.

Find the scalar components and magnitude of the vector joining the points $P(x_1, y_1, z_1)$ and $Q(x_2, y_2, z_2)$.

Find the integrals of the functions in Exercises:
$\frac{\sin^3\text{x}+\cos^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}$

Prove that 1, 1, 1 cannot be direction cosines of a straight line.

Find the values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and $\mathrm{d}$ from the equation $\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]$.