If A = [ ll 3 & 2 1 & 4 ], then write the value of A .(adj A ). - Vidyadip

Question

If $A =\left[\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right]$, then write the value of $A .(\operatorname{adj} A )$.

✓

Answer

$A_{11}=4, A_{12}=-1, A_{21}=-2, A_{22}=3$$
\begin{aligned}
\operatorname{adj} A & =\left[\begin{array}{cc}
4 & -1 \\
-2 & 3
\end{array}\right]^{\prime}=\left[\begin{array}{cc}
4 & -2 \\
-1 & 3
\end{array}\right] \\
\text { A. }(\operatorname{adj} A) & =\left[\begin{array}{ll}
3 & 2 \\
1 & 4
\end{array}\right]\left[\begin{array}{cc}
4 & -2 \\
-1 & 3
\end{array}\right] \\
& =\left[\begin{array}{cc}
10 & 0 \\
0 & 10
\end{array}\right] \text {}
\end{aligned}
$

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 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

Evaluate the integral $\int_{0}^{\frac{\pi}{2}} \frac{\sin x}{1+\cos ^{2} x} d x$ using substitution.

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{25\pi}{6}\Big)$

Let $R$ = {$(x, y): |x^2 - y^2| < 1$} be a relation on set $A$ = {$1, 2, 3, 4, 5$}. Write $R$ as a set of ordered pairs.

Solve the following differential equations:
$(\text{y}^2+1)\text{dx}-(\text{x}^2+1)\text{dy}=0$

Evaluate$:- \tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\tan ^{-1}\left(\sin \left(-\frac{\pi}{2}\right)\right)$

If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=\cos\theta-\cos2\theta,\text{y}=\sin\theta-\sin2\theta$

If $A$ and $B$ are square matrices of the same order, explain, why in general:
$(A + B)(A - B) \neq A^2 - B^2.$

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cap\overline{\text{B}})$

A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that,
Only one of them will be selected?

Evaluate the following integrals:
$\int\limits^\frac{\pi}{4}_0\tan\text{x dx}$