Construct a 2 × 2 matrix A = [aij] whose elements aij are given b… - Vidyadip

Question

Construct a 2 × 2 matrix A = [a_ij] whose elements a_ij are given by:
$\text{a}_\text{ij}=\frac{|-3\text{i}-\text{j}|}{2}$

✓

Answer

Here,
$\text{a}_{11}=\frac{|-3(1)+1|}{2}=\frac{|-3+1|}{2}=\frac{|-2|}{2}=1,$ $\text{a}_{12}=\frac{|-3(1)+2|}{2}=\frac{|-3+2|}{2}=\frac{|-1|}{2}=\frac{1}{2}$
$\text{a}_{21}=\frac{|-3(2)+1|}{2}=\frac{|-6+1|}{2}=\frac{|-5|}{2}=\frac{5}{2},$ $\text{a}_{22}=\frac{|-3(2)+2|}{2}=\frac{|-6+2|}{2}=\frac{|-4|}{2}=2$
So, the required matrix is $\begin{bmatrix}1&\frac{1}{2}\\\frac{5}{2}&2\end{bmatrix}.$

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" from Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the principal values:
$\sec^{-1}\bigg(\frac{2}{\sqrt{3}}\bigg)$

The probability distribution of random variable X is given below:

$\text{X}$	$0$	$1$	$2$	$3$
$\text{P}(\text{X})$	$\text{k}$	$\frac{\text{k}}{2}$	$\frac{\text{k}}{4}$	$\frac{\text{k}}{8}$

Determine $\text{P}(\text{X}\leq2)$ and $\text{P}(\text{X}>2)$

Find $\vec{\text{a}}.\vec{\text{b}}$ when
$\vec{\text{a}}=\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+3\hat{\text{j}}-2\hat{\text{k}}$

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, -1), (4, 3, -1).

If $\text{A}=\begin{bmatrix}4&3\\1&2 \end{bmatrix}$ and $\text{B}=\begin{bmatrix}-4\\3\end{bmatrix},$ write AB.

Evaluate the definite integral in Exercise:
$\int_{2}^{3}\frac{1}{\text{x}}\text{dx}$

If $\text{A}=\begin{bmatrix}5&3&8\\2&0&1\\1&2&3\end{bmatrix}.$ Write the cofactor of element a₃₂.

If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are non-coplanar vectors, prove that the given vectors are non-coplanar:
$2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}},\ \vec{\text{a}}+\vec{\text{b}}-2\vec{\text{c}}$ and $\vec{\text{a}}+\vec{\text{b}}-3\vec{\text{c}}$

Evaluate the following definite integrals:
$\int_{4}\limits^{9}\frac{1}{\sqrt{\text{x}}} \text{ dx}$

Let A and B be two independent events such that P(A) = p₁ and P(B) = p₂. Describe in words the events whose probabilities are:
p₁p_2.