Solve system of linear equations, using matrix method. 5 x+2 y=4 … - Vidyadip

MCQ

Solve system of linear equations, using matrix method. $5 x+2 y=4 ; 7 x+3 y=5$

A
$x=-2,y=-3$
✓
$x=2,y=-3$
C
$x=2,y=3$
D
$x=-2,y=3$

✓

Answer

Correct option: B.

$x=2,y=-3$

The given system of equation can be written in the form of $A X=B,$
where$A=\left[\begin{array}{ll}5 & 2 \\ 7 & 3\end{array}\right], X=\left[\begin{array}{l}x \\ y\end{array}\right]$ and $B=\left[\begin{array}{l}4 \\ 5\end{array}\right]$
Now $|A|=15-14=1 \neq 0$
Thus, $A$ is non $-$ singular.
Therefore, its inverse exists.
Now,
$A^{-1}=\frac{1}{|\mathrm{A}|}(\operatorname{adj} A)$
$\therefore A^{-1}=\left[\begin{array}{cc}3 & -2 \\ -7 & 5\end{array}\right]$
$\therefore X=A^{-1} B=\left[\begin{array}{cc}3 & -2 \\ -7 & 5\end{array}\right]\left[\begin{array}{l}4 \\ 5\end{array}\right]$
$\Rightarrow\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}12-10 \\ -28+25\end{array}\right]=\left[\begin{array}{c}2 \\ -3\end{array}\right]$
Hence, $x=2$ and $y=-3$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $f(x)=\int_{0}^{x} e^{t} f(t) d t+e^{x}$ be a differentiable function for all $x \in R$. Then $f(x)$ equals ..... .

If ${\cos ^{ - 1}}\left( {\frac{1}{x}} \right) = \theta $, then $\tan \theta =$

The probability of getting $4$ heads in $8$ throws of a coin, is

Let $A = \int\limits_0^1 \, \frac{{{e^t}\,\,\,d\,t}}{{1\,\, + \,\,t}}$ then $\int\limits_{a - 1}^a {\,\,\frac{{{e^{ - t}}\,dt}}{{t\, - \,a\, - \,1}}} $ has the value

The locus of feet of perpendicular from either foci of the ellipse

$(x - y +1)^2 + (2x + 2y - 6)^2 = 20$ on any tangent will be

If $\omega $ is a complex cube root of unity, then $225 + $${(3\omega + 8{\omega ^2})^2}$$ + {(3{\omega ^2} + 8\omega )^2} = $

Solution of the differential equation
$\left( {{e^{{x^2}}} + {e^{{y^2}}}} \right)\,y\,\frac{{dy}}{{dx}} + {e^{{x^2}}}(x{y^2} - x)= 0,$ is

Let $A_1, A_2, A_3$ be the three A.P. with the same common difference $d$ and having their first terms as $A , A +1, A +2$, respectively. Let $a , b , c$ be the $7^{\text {th }}, 9^{\text {th }}, 17^{\text {th }}$ terms of $A_1, A_2, A_3$, respectively such that $\left|\begin{array}{lll} a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1\end{array}\right|+70=0$ If $a=29$, then the sum of first $20$ terms of an $AP$ whose first term is $c - a - b$ and common difference is $\frac{ d }{12}$, is equal to $........$.

Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^3y^4z^5 = (0. 1 ) (600)^3$. Then $x^3 + y^3 + z^3$ is equal to

${d \over {dx}}\{ \cos (\sin {x^2})\} = $