Download App

MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES2 Marks
Question
Construct a 2 × 2 matrix, A = $[\text{a}_{\text{ ij}}]$, whose elements are given by:$\text {a}_\text {ij}=\frac {(\text{i}+2 \text{j})^{2}}{2} $
✓

Answer

$\text A=\left[\text {a}_{\text {ij}} \right]\text{is}\ 2\times2\ {\text {matrix where}}\ \text {a}_{\text {ij}}=\frac{(\text{i}+2 \text{j})^{2}}{2}$$\therefore\ \text{a}_{11}=\frac{(1+2)^2}{2}=\frac{9}{2}$, $\text{a}_{12}=\frac{(1+4)^2}{2}=\frac{25}{2}$
$\text{a}_{21}=\frac{(2+2)^2}{2}=\frac{16}{2}=8,$ $\text{a}_{22}=\frac{(2+4)^2}{2}=\frac{36}{2}=18 $
$\therefore\ \ \text{A}=\begin{bmatrix}\frac{9}{2}& \frac{25}{2} \\8 & 18 \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

Evaluate the following integrals:$\int\text{e}^{\text{x}}\Big(\frac{\text{x}-1}{2\text{x}^2}\Big)\text{dx}$
→
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are the position vectors of the vertices of a triangle, then write the position vector of its centroid.
→
Integrate the function in exercise.
$\text{x} \ \sin\text{x}$
→
In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $\frac{3}{4}$ be the probability that he knows the answer and $\frac {1}{4}$ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $\frac{1}{4}$. What is the probability that the student knows the answer given that he answered it correctly?
→
If $\text{x}=\text{f}(\text{t})$ and $\text{y}=\text{g}(\text{t}),$ then write the value of $\frac{\text{d}^2\text{y}}{\text{dx}^2}.$
→
Find the general solution of the differential equation $\frac{{dy}}{{dx}} = \frac{{1 - \cos x}}{{1 + \cos x}}$
→
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that
only 3 cards are spades?
→
Find the second order derivatives of the function given in Exercise:
$\tan^{-1}\text{x}$
→
Define differentiability of a function at a point.
→
Differentiate w.r.t. x, the function,$\sqrt{3 x+2}+\frac{1}{\sqrt{2 x^{2}+4}}$
→