Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 Marks
Question
construct a $2×2$ matrix $A = [a_{ij}]$ whose elemants $a_{ij}$ are given by $a_{ij}$ $=\begin{cases}\frac{|-3\text{i}+\text{j}|}{2},&\text{if i }\neq\text{j}\\{i}+\text{j})^2,&\text{if i }=\text{j}\end{cases}$
✓

Answer

Let us the matrix be $\text{A}=\begin{bmatrix}\text{a}_{11}&\text{a}_{12}\\\text{a}_{21}&\text{a}_{22} \end{bmatrix}$ For the entries $a_{12}$ and $a_{21}$ we have i $\neq$ j, so by the Condition we have $\text{a}_{12}=\frac{|-3\text{i}+\text{j}|}{2},\text{ a}_{21}=\frac{|-3\text{i}+\text{j}|}{2}$ $\Rightarrow\text{a}_{12}=\frac{|-3+2|}{2},\text{ a}_{21}=\frac{|-3.2+1|}{2}$ $\Rightarrow\text{a}_{12}=\frac{|-1|}{2},\text{ a}_{21}=\frac{|-5|}{2}$ $\Rightarrow\text{a}_{12}=\frac{1}{2},\text{ a}_{21}=\frac{5}{2}$ For the entries $a_{11}$ and $a_{22}$ we have i = j, so by the given condition we have $\Rightarrow\text{a}_{11}=(\text{i + j})^2, \text{ a}_{22}=(\text{i + j})^2$ $\Rightarrow\text{a}_{11}=(1+1)^2,\text{ a}_{22}=(2+2)^2$ $\Rightarrow\text{a}_{11}=4,\text{ a}_{22}=16$ So, $\text{A}=\begin{bmatrix}4&\frac{1}{2}\\\frac{5}{2}&16 \end{bmatrix}$

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 "3 Marks Question" 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

Show that the normals to the following parirs of planes are perpendicular other.
x - y + z - 2 = 0 and 3x + 2y - z + 4 = 0
→
Evaluate the following integrals:
$\int\Big(\frac{\text{x}+1}{\text{x}}\Big)(\text{x}+\log\text{x})^2\text{dx}$
→
Differentiate the following w.r.t. x:
$\frac{8^\text{x}}{\text{x}^8}$
→
Prove that the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector.
→
Show that $\text{f}\text{(x)}=\begin{cases}1+\text{x}^2,&\text{if } 0\leq\text{x}\leq 1\\2-\text{x},&\text{if }\text{x} > 1\end{cases}$ is discontinuous at x = 1.
→
Differentiate the following functions with respect to x:
$3^{\text{x}^2+2\text{x}}$
→
A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
→
Prove that the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector.
→
Write the maximum value of $\text{f}(\text{x})=\frac{\log\text{x}}{\text{x}}$, if it exists.
→
Find fog and gof if:$f(x) = x + 1, g(x) = e^x$​​​​​​​
→