Let A = 2 & -1 3 & 4 , = B = 5 & 2 7 & 4 , C = 2 & 5 3 & 8 ,find … - Vidyadip

Question

$\text{Let A} = \begin{pmatrix} 2 & -1 \\ 3 & 4 \\ \end{pmatrix}, = \text{B} = \begin{pmatrix} 5 & 2 \\ 7 & 4 \\ \end{pmatrix}, \text{C} = \begin{pmatrix} 2 & 5 \\ 3 & 8 \\ \end{pmatrix},$find a matrix D such that CD – AB = O.

✓

Answer

$\text{Let D} = \begin{bmatrix} \text{x} & \text{y} \\ \text{z} & \text{w}\\ \end{bmatrix}$
$\text{CD} = \text{AB} \Rightarrow\begin{bmatrix} \text{2x + 5z} & \text{2y + 5w} \\ \text{3x + 8z} & \text{3y + 8w}\\ \end{bmatrix} = \begin{bmatrix} 3 & 0 \\ 43 & 22\\ \end{bmatrix}$
$\text{2x + 5z = 3, 3x + 8z = 43; 2y + 5w = 0, 3y + 8w = 22.}$
$\text{Solving, we get x = –191, y = –110, z = 77, w = 44}$
$\therefore \text{D} = \begin{bmatrix} -191 & -110\\ 77 & 44\\ \end{bmatrix}$

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

Differentiate the following functions with respect to x:
$\sqrt{\frac{1-\text{x}^2}{1+\text{x}^2}}$

Show that in any triangle ABC a = b cos C + c cos B

Evaluate the following integrals:
$\int\limits^{\pi}_0\text{x}\cos^2\text{x dx}$

Using properties of determinants, solve the following for x:

$ \begin{vmatrix} \text{x - 2} & \text{2x - 3 } & \text{3x - 4 } \\ \text{x - 4} & \text{2x - 9} & \text{2x - 16} \\ \text{x -8} & \text{2x - 27} & \text{3x -64} \end{vmatrix}=0$

Find the mean number of heads in three tosses of a fair coin.

Find the distance of the point (-1, -5, -10) from the point of intersection of the line $\vec{\text{r}}=(2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}})+\lambda(3\hat{\text{i}}+4\hat{\text{j}}+2\hat{\text{k}})$ and the plane $\vec{\text{r}}\cdot(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}})=5.$

Solve the following determinant equations:
$\begin{vmatrix}1&\text{x}&\text{x}^3\\1&\text{b}&\text{b}^3\\1&\text{c}&\text{c}^3\end{vmatrix}=0,\text{b}\neq\text{c}$

$\begin{vmatrix}-\text{a}(\text{b}^2+\text{c}^2-\text{a}^2)&2\text{b}^3&2\text{c}^3\\2\text{a}^3&-\text{b}(\text{c}^2+\text{a}^2-\text{b}^2)&2\text{c}^3\\2\text{a}^3&2\text{b}^3&-\text{c}(\text{a}^2+\text{b}^2-\text{c}^2)\end{vmatrix}$
$=\text{abc}(\text{a}^2+\text{b}^2+\text{c}^2)$

Using differentials, find the approximate values of the following:
$\frac{1}{(2.002)^2}$

Find the area enclosed by the parabola y = 5x² and y = 2x² + 9.