Write A-1 for A= 2 & 5 1 & 3 - Vidyadip

Question

Write A^-1 for $\text{A}=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$

✓

Answer

$|\text{A}|=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}=1\neq0$
Let C_ij be the cofactor of a_ij in A.
The cofactors of element A are given by
C₁₁ = 3
C₁₂ = -1
C₂₁ = -5
C₂₂ = 2
$\text{adj A}=\begin{bmatrix} 3 & -1 \\ -5 & 2 \end{bmatrix}^\text{T}=\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}$
$|\text{A}|=6-5=1$
$\therefore\text{A}^{-1}=\frac{1}{|\text{A}|}\text{ adj A}=\begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}$

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" from DETERMINANTS→DETERMINANTS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let * be a binary operation, on the set of all non-zero real numbers, given by
$\text{a}\times\text{b}=\frac{\text{ab}}{5}\ \forall\text{ a, b}\in\text{R}-\{0\}$
Write the value of x given by 2 * (x * 5) = 10.

$\text{If}\ \text{A}'=\begin{bmatrix}-2&3\\1&2\end{bmatrix}, \text{and}\ \text{B}=\begin{bmatrix}-1&0\\1&2\end{bmatrix}\ \text{then find}\ (\text{A} + 2\text{B})'$

Show that the following triads of vectors are coplanar:
$\vec{\text{a}}=-4\hat{\text{i}}-6\hat{\text{j}}-2\hat{\text{k}},\vec{\text{b}}=-\hat{\text{i}}+4\hat{\text{j}}+3\hat{\text{k}},\vec{\text{c}}=-8\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}}$

Evaluate the integral $\int_{-1}^{1} \frac{d x}{x^{2}+2 x+5}$ using substitution.

Write A^-1 for $\text{A}=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$

Find the values of x and y, if $2\begin{bmatrix}1&3\\0&\text{x} \end{bmatrix}+\begin{bmatrix}\text{y}&0\\1&2 \end{bmatrix}=\begin{bmatrix}5&6\\1&8 \end{bmatrix}$

Evaluate the following integrals:
$\int(3\text{x}+4)^2\text{dx}$

Evaluate the following integrals:
$\int\Big(\frac{\text{m}}{\text{x}}+\frac{\text{x}}{\text{m}}+\text{m}^\text{x}+\text{x}^\text{m}+\text{mx}\Big)\text{dx}$

Evaluate the following integrals:
$\int\frac{1}{\text{x}^5}\text{dx}$

Write the equation of the plane passing through (2, −1, 1) and parallel to the plane 3x + 2y − z = 7.