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 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 Questions" 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

For the following differntial equations verify that the accompanying function is a solution:

Differential equation	Function
$\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}$	$\text{y}=\text{ax}$

If $f : R → R$ be defined by $f(x) = x^4,$ write $f^{-1}(1).$

Let * be a binary operation on the set Q of rational numbers as follows:
a * b = a – b

Find the value of x from the following: $\begin{vmatrix}\text{x}&4\\2&2\text{x}\end{vmatrix}=0$

Find $\frac{d y}{d x}$, if y + sin y = cos x.

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

Let '*' be a binary operation on N defined by a * b = 1.c.m. (a, b) for all $\text{a, b}\in\text{N}$
Find 2 * 4, 3 * 5, 1 * 6.

Evaluate:
$\int\sqrt{\frac{1-\cos\ 2\text{x}}{2}}\text{dx}$

If $\text{A}=\begin{bmatrix} 1 & -3 \\ 2 & 0 \end{bmatrix},$ write adj A.

Evaluate the product $(3 \vec{a}-5 \vec{b}) \cdot(2 \vec{a}+7 \vec{b})$