If A= 2&-1 3&2 and B= 0&4 -1&7 , find 3A2 - 2B + l - Vidyadip

Question

If $\text{A}=\begin{bmatrix}2&-1\\3&2 \end{bmatrix} $ and $\text{B}=\begin{bmatrix}0&4\\-1&7\end{bmatrix} ,$ find 3A² - 2B + l

✓

Answer

Given: $\text{A}=\begin{bmatrix}2&-1\\3&2 \end{bmatrix}$
Now,
$\text{A}^2=\text{AA}$
$\Rightarrow\text{A}^2=\begin{bmatrix}2&-1\\3&2 \end{bmatrix}\begin{bmatrix}2&-1\\3&2 \end{bmatrix}$
$\Rightarrow\text{A}^2=\begin{bmatrix}4-3&-2-2\\6+6&-3+4 \end{bmatrix}$
$\Rightarrow\text{A}^2=\begin{bmatrix}1&-4\\12&1 \end{bmatrix}$
$3\text{A}^2-2\text{B}+\text{I}$
$\Rightarrow3\text{A}^2-2\text{B}+\text{I}=3\begin{bmatrix}1&-4\\12&1 \end{bmatrix}-2\begin{bmatrix}0&4\\-1&7 \end{bmatrix}+\begin{bmatrix}1&0\\0&1 \end{bmatrix}$
$\Rightarrow3\text{A}^2-2\text{B}+\text{I}=\begin{bmatrix}3&-12\\36&3 \end{bmatrix}-\begin{bmatrix}0&8\\-2&14 \end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}$
$\Rightarrow3\text{A}^2-2\text{B}+\text{I}=\begin{bmatrix}3-0+1&-12-8+0\\36+2+0&3-14+1\end{bmatrix}$
$\Rightarrow3\text{A}^2-2\text{B}+\text{I}=\begin{bmatrix}4&-20\\38&-10 \end{bmatrix}$

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 "4 Marks" 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

A firm manufactures two products A and B. Each product is processed on two machines M₁ and M₂. Product A requires 4 minutes of processing time on M₁ and 8 min. on M₂; product B requires 4 minutes on M₁ and 4 min. on M₂. The machine M₁ is available for not more than 8 hrs 20 min. while machine M₂is available for 10 hrs. during any working day. The products A and B are sold at a profit of Rs. 3 and Rs. 4 respectively.
Formulate the problem as a linear programming problem and find how many products of each type should be produced by the firm each day in order to get maximum profit.

Find the equation of the tangent to the curve x² + 3y − 3 = 0, which is parallel to the line y = 4x − 5.

If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=\frac{\sin^3\text{t}}{\sqrt{\cos2\text{t}}},\text{y}\frac{\cos^3\text{t}}{\sqrt{\cos2\text{t}}}$

Show that the lines$\frac{\text{X} + 1 }{3} =\frac{\text{y} + 3}{5} = \frac{\text{z} + 5}{7}\text{ and } \frac{\text{x} - 2}{1} =\frac{\text{y} - 4}{3} =\frac{\text{z} - 6 }{5}$ intersect. Also find their point of intersection.

Differentiate the following functions with respect to x:
$\tan^{-1}\Big(\frac{5\text{x}}{1+6\text{x}^3}\Big), -\frac{1}{\sqrt{6}}<\text{x}<\frac{1}{\sqrt{6}}$

If $A =\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]$, then, prove that $A^3-6 A^2+7 A+2 I=O$ and hence find $A^{-1}$.

Show that the differential equation of $y' = \frac{{x + y}}{x}$, is homogeneous and solve it.

Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}1&\text{a}&\text{bc}\\1&\text{b}&\text{ca}\\1&\text{c}&\text{ab} \end{vmatrix}$

Show that $\text{f}(\text{x})=\text{x}^\frac{1}{3}$ is not differentible at x = 0.

Find the area of the region $\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\leq4,\text{x}+\text{y}\geq2\}$