Find the non-zero values of x satisfying the matrix equation x [ … - Vidyadip

Question

Find the non-zero values of $x$ satisfying the matrix equation
$
x\left[\begin{array}{cc}
2 x & 2 \\
3 & x
\end{array}\right]+2\left[\begin{array}{cc}
8 & 5 x \\
4 & 4 x
\end{array}\right]=2\left[\begin{array}{cc}
x^2+8 & 24 \\
10 & 6 x
\end{array}\right]
$

✓

Answer

$
\begin{aligned}
& x\left[\begin{array}{cc}
2 x & 2 \\
3 & x
\end{array}\right]+2\left[\begin{array}{ll}
8 & 5 x \\
4 & 4 x
\end{array}\right]=2\left[\begin{array}{cc}
x^2+8 & 24 \\
10 & 6 x
\end{array}\right] \\
& {\left[\begin{array}{cc}
2 x^2 & 2 x \\
3 x & x^2
\end{array}\right]+\left[\begin{array}{cc}
16 & 10 x \\
8 & 8 x
\end{array}\right]=\left[\begin{array}{cc}
2 x^2+16 & 48 \\
20 & 12 x
\end{array}\right]} \\
& {\left[\begin{array}{cc}
2 x^2+16 & 12 x \\
3 x+8 & x^2+8 x
\end{array}\right]=\left[\begin{array}{cc}
2 x^2+16 & 48 \\
20 & 12 x
\end{array}\right]} \\
& 12 x=48 \\
& x=\frac{48}{12} \\
& =4
\end{aligned}
$
The value of $x=4$

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 "[5 Mark Questions]" from Algebra→Algebra — all question types→MATHS STD 10 question papers→Tamilnadu Board STD 10 question papers→Tamilnadu Board question paper generator→

Similar questions

Vani, her father and her grandfather have an average age of 53. One-half of her grandfather’s age plus one-third of her father’s age plus one-fourth of Vani’s age is 65. Four years ago if Vani’s grandfather was four times as old as Vani then how old are they all now?

In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number

An Emu which is 8 feet tall is standing at the foot of a pillar which is 30 feet high. It walks away from the pillar. The shadow of the Emu falls beyond Emu. What is the relation between the length of the shadow and the distance from the Emu to the pillar?

Find the square root of the following polynomials by division method
$37 x^2-28 x^3+4 x^4+42 x+9$

Graph the following quadratic equation and state their nature of solution
$x^2$ + x + 7 = 0

A metallic sheet in the form of a sector of a circle of radius 21 cm has a central angle of $216^{\circ}$ The sector is made into a cone by bringing the bounding radii together. Find the volume of the cone formed.

Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of $\frac{20 km }{ hr }$ and the second train travels at $\frac{30 km }{ hr }$. After 2 hours, what is the distance between them?

Prove the following identities. $\sqrt{\frac{1+\sin \theta}{1-\sin \theta}}+\sqrt{\frac{1-\sin \theta}{1+\sin \theta}}=2 \sec \theta$

If $a, b, c$ is three consecutive terms of an A.P. and $x, y, z$ are three consecutive terms of a G.P. then prove that $x^{b-c} \times y^{c-a} \times z^{a-b}$ $=1$

Prove that $n^2-n$ divisible by 2 for every positive integer $n$