Solve the system of linear equation, using matrix method 5x + 2y … - Vidyadip

Question

Solve the system of linear equation, using matrix method $5x + 2y = 3; 3x + 2y = 5$

✓

Answer

Matrix form of given equations is $ AX = B$
$\Rightarrow \left[ {\begin{array}{*{20}{c}} 5\ \ 2 \\ 3\ \ 2 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 3 \\ 5 \end{array}} \right]$
Here $A = \left[\begin{array}{ll} 5\ \ 2 \\ 3\ \ 2 \end{array}\right], X = \left[\begin{array}{l} x \\ y \end{array}\right]$ and $B = \left[\begin{array}{l} 3 \\ 5 \end{array}\right]$
$\therefore |A| = \left|\begin{array}{ll} 5\ \ 2 \\ 3\ \ 2 \end{array}\right| = 10 - 6 = 4 \ne 0$
Therefore, solution is unique and $X = A^{-1}B = \frac{1}{|A|} (\text{adj}\ A B)$
$ = \left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right] = \frac{1}{4}\left[ {\begin{array}{*{20}{c}} 2&-2 \\ { - 3}5 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 3 \\ 5 \end{array}} \right]$
$= \frac{1}{4}\left[ {\begin{array}{*{20}{c}} {6 - 10} \\ { - 9 + 25} \end{array}} \right] = \frac{1}{4}\left[ {\begin{array}{*{20}{c}} { - 4} \\ {16} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 1} \\ 4 \end{array}} \right]$
Therefore, $x = -1$ and $y = 4$

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 "3 Marks Question" from Determinants→Determinants — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

$\begin{array}{l}\text { Verify } A(\text { adj. A) }=(\operatorname{adj} . A) A=|A| \text { : } \\ {\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 0 & -2 \\ 1 & 0 & 3\end{array}\right]}\end{array}$

Find the mean and standard deviation of the following probability distributions:

$x_i$	$1$	$2$	$3$	$4$
$p_i$	$0.4$	$0.3$	$0.2$	$0.1$

Evaluate the following integrals:$\int\text{x}^3\cos\text{x}^2\text{dx}$

Evaluate $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\tan x}}$

Evalute the following integrals:
$\int\frac{\sec\text{x}}{\sec2\text{x}}\text{dx}$

Reduce the equation of the following planes to intercept from and find the intercepts on the coordinate axes:
4x + 3y - 6z - 12 = 0

At what points on the following curves, is the tangent parallel to x-axis?
$\text{y}=\text{x}^2\text{ on }[-2,2]$

Write the vector equation of the line passing through the point (1, -2, -3) and normal to the plane $\vec{\text{r}}.(2\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}})=5.$

Evaluate the following integrals:
$\int\text{x}^3\sin\text{x}^4\text{dx}$

If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.