Given [ cc 2 & 1 -3 & 4 ], X= [ l 7 6 ] the matrix X - Vidyadip

Question

Given $\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right], X=\left[\begin{array}{l}7 \\ 6\end{array}\right]$ the matrix $X$

✓

Answer

We have
$ \left[\begin{array}{cc} 2 & 1 \\ -3 & 4 \end{array}\right], X =\left[\begin{array}{l} 7 \\ 6 \end{array}\right]$ Let $X =\left[\begin{array}{l}x \\ y\end{array}\right]$
So, $\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}7 \\ 6\end{array}\right]$
$ \Rightarrow\left[\begin{array}{c} 2 x+y \\ -3 x+4 y \end{array}\right]=\left[\begin{array}{l} 7 \\ 6 \end{array}\right] $
Multiplying $(i)$ by $3$ and $(ii)$ by $2,$ and adding we get:
$6 x+33 y=21$
$ -6 x+8 y=12$
$ 11 y=33$
$ \Rightarrow y =3$
From $(i),$
$2 x=7-3=4$
$ \Rightarrow x=2$
So, $X=\left[\begin{array}{l}2 \\ 2\end{array}\right]$.

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 sum]" from Matrices→Matrices — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

If a : b : : c : d, prove that (2a + 3b)(2c – 3d) = (2a – 3b)(2c + 3d)

Given that $x \in I$, solve the inequation and graph the solution on the number line:
$
3 \geq \frac{x-4}{2}+\frac{x}{3} \geq 2
$

Find the sum of G.P.:

0.3 + 0.03 + 0.003 + 0.0003 +….. to 8 items.

Find the equation of the line passing through: $(−1, −4)$ and $(3, 0)$

Find the equation of the line through the points A(-1,3) and B(0,2). Hence, show that the pointA,B and C (1,1) are collinear.

If $A =\left[\begin{array}{ll}1 & 4 \\ 1 & 0\end{array}\right], B =\left[\begin{array}{cc}2 & 1 \\ 3 & -1\end{array}\right]$ and $C =\left[\begin{array}{ll}2 & 3 \\ 0 & 5\end{array}\right]$ compute $( AB ) C$ $=(C B) A$ ?

Two cars start together in the same direction from the same place. The first cargoes at uniform speed of $10\ km h^{-1}$. The second car goes at a speed of $8\ km h^{-1}$ in the first hour and thereafter increasing the speed by $0.5\ km h^{-1}$ each succeeding hour. After how many hours will the two cars meet?

The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.

Solve equation using factorisation method:
$x+\frac{1}{x}=2.5$

Find the duplicate ratio of the following :
$(a+b): (a^2- b^2)$