Construct a 3 × 4 matrix A = [aij] whose element aij are given by… - Vidyadip

Question

Construct a 3 × 4 matrix A = [a_ij] whose element a_ij are given by:
a_ij = 2i

✓

Answer

Here, $\text{A}=(\text{a}_\text{ij})_{3\times4}=\begin{bmatrix}\text{a}_{11}&\text{a}_{12}&\text{a}_{13}&\text{a}_{14}\\\text{a}_{21}&\text{a}_{22}&\text{a}_{23}&\text{a}_{24}\\\text{a}_{31}&\text{a}_{32}&\text{a}_{33}&\text{a}_{34}\end{bmatrix}\ \dots(1)$
a₁₁ = 2(1) = 2, a₁₂ = 2(1) = 2, a₁₃ = 2(1) = 2, a₁₄ = 2(1) = 2
a₂₁ = 2(2) = 4, a₂₂ = 2(2) = 4, a₂₃ = 2(2) = 4, a₂₄ = 2(2) = 4
a₃₁ = 2(3) = 6, a₃₂ = 2(3) = 6, a₃₃ = 2(3) = 6 and a₃₄ = 2(3) = 6
So, the required matrix is $\begin{bmatrix}2&2&2&2\\4&4&4&4\\6&6&6&6\end{bmatrix}.$

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 "1 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

How many arbitray constants are there in the genral solution of the differential equation of orader 3.

Find the order and degree, if defined, of the differential equation $\frac{d y}{d x}-\cos x=0$

Determine order and degree (if defined) of differential equations given in Exercise.
y' + y = e^x

Evaluate the definite integral $\int_{0}^{1} \frac{d x}{\sqrt{1+x}-\sqrt{x}}$

Integrate the functions in Exercises:
$\sin(\text{ax+b})\cos(\text{ax+b})$

The vector directed from A to B and joining the points $A (1,2,2)$ and $B (2,3,1)$ is :

Write an anti derivative of function using the method of inspection: $\frac{1}{x}, x \neq 0$

Find the direction cosines of line $\frac{x-2}{3}=\frac{2 y-4}{6}=\frac{z-1}{-3}$

Prove that: ${\tan ^{ - 1}}\frac{{63}}{{16}} = {\sin ^{ - 1}}\frac{5}{{13}} + {\cos ^{ - 1}}\frac{3}{5}$

Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table (Table 1.2).
Is * commutative?
(Hint: use the following table)

*	1	2	3	4	5
1	1	1	1	1	1
2	1	2	1	2	1
3	1	1	3	1	1
4	1	2	1	4	1
5	1	1	1	1	5