Download App

Adjoint and Inverse of a Matrix — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAdjoint and Inverse of a Matrix2 Marks
Question
Write the adjoint of the matrix $\text{A}=\begin{bmatrix} -3 & 4 \\ 7 & -2 \end{bmatrix}$.
✓

Answer

Let $C_{ij}$ be a cofactor of $a_{ij}$ in A. Now, $C_{11} = -2 C_{12} = -7 C_{21} = -4 C_{22} = -3$
$\therefore\ \text{adj A}=\begin{bmatrix} -2 & -7 \\ -4 & -3 \end{bmatrix}^\text{T}=\begin{bmatrix} -2 & -4 \\ -7 & -3 \end{bmatrix}$

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 Adjoint and Inverse of a Matrix→Adjoint and Inverse of a Matrix — 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 set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.
→
If f'(1) = 2 and $\text{y}=\text{f}(\log_\text{e}\text{x}),$ find $\frac{\text{d}}{\text{dx}}\text{at x}=\text{e}.$
→
Write the angle between the vectors $\vec{\text{a}}\times\vec{\text{b}}$ and $\vec{\text{b}}\times\vec{\text{a}}.$
→
Let $\text{f}:\text{R}-\Big\{-\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be a function defined as $\text{f(x)}=\frac{2\text{x}}{5\text{x}+3}.$ Write $f^{-1}$​​​​​​​: Range of $\text{f}\rightarrow\ \text{R}-\Big\{-\frac{3}{5}\Big\}.$
→
Determine the direction cosines of the normal to the plane and the distance from the origin.
x + y + z
→
Find the principal values:
$\text{cosec}^{-1}(-\sqrt{2})$
→
Write tha value of $\int\sec\text{x}(\sec\text{x}+\tan\text{x})\text{dx}$
→
Let $f: X → Y$ be an invertible function. Show that f has unique inverse. $($Hint: suppose $g_1$ and $g_2$ are two inverses of f. Then for all $y \in Y, fog_1(y) = 1_Y(y) = fog_2(y).$ Use one-one ness of $f).$
→
Express matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{rr} {1} & {5} \\ {-1} & {2} \end{array}\right]$
→
Find the values of 'a' for which the vectors
$\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}+\hat{\text{k}},\vec\beta={\text{a}}\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$ and $\vec\gamma=\hat{\text{i}}+2\hat{\text{j}}+\text{a}\hat{\text{k}}$ are coplanar.
→