Skip to content
ICSEClass 10MathematicsMatrices03 Mark2024 Moderate

QQuestion

A = \begin{bmatrix}x & 0 \\ 1 & 1\end{bmatrix}, B = \begin{bmatrix}4 & 0 \\ y & 1\end{bmatrix} and C = \begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix}.

Find the values of x and y, if AB = C.

Exam-ready answer • 03 Mark

Answer

Given, AB = C.

\begin{bmatrix}x & 0 \\ 1 & 1\end{bmatrix}\begin{bmatrix}4 & 0 \\ y & 1\end{bmatrix}=\begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix}

Multiplying the matrices:

\begin{bmatrix}(x\times4)+(0\times y) & (x\times0)+(0\times1) \\ (1\times4)+(1\times y) & (1\times0)+(1\times1)\end{bmatrix}=\begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix} \begin{bmatrix}4x & 0 \\ 4+y & 1\end{bmatrix}=\begin{bmatrix}4 & 0 \\ x & 1\end{bmatrix}

Equating corresponding elements:

4x = 4

⇒ x = 1

Also, 4 + y = x

⇒ 4 + y = 1

⇒ y = 1 − 4

⇒ y = −3

Therefore, x = 1 and y = −3.

Was this answer helpful?

Related Questions

More ICSE Moderate level questions

1/12

If A = and A² = , then the value of x is: (a) 2 (b) 4 (c) 8 (d) 10

Easy 01 Mark

If find A(B + C) − 14I.

Easy 03 Mark

If A = , then A² is equal to: (a) (b) (c) (d)

Easy 01 Mark

If , the values of x and y respectively are: (a) 1, −2 (b) −2, 1 (c) 1, 2 (d) −2, −1

Easy 01 Mark

If A = , B = and AB = , find the values of a and b.

Hard 04 Mark

If A = and B = , then the order of AB is: (a) 2 × 2 (b) 2 × 1 (c) 1 × 2 (d) AB is not possible

Easy 01 Mark

If A = , B = and C = , find: (a) A + C (b) B(A + C) (c) 5B (d) B(A + C) − 5B

Hard 05 Mark

Solve the following quadratic equation for x and give your answers correct to three significant figures: 2x² − 10x + 5 = 0

Moderate 03 Mark

Mr Gupta invested ₹33,000 in buying ₹100 shares of a company at 10% premium. The dividend declared by the company is 12%. Find: (a) the number of shares purchased by him. (b) his annual dividend.

Moderate 03 Mark

The letters A, D, M, N, O, S, U and Y of the English alphabet are written on separate cards and put in a box. The cards are well shuffled and one card is drawn at random. What is the probability that the card drawn is a letter: (a) of the word MONDAY? (b) which does not appear in MONDAY? (c) which appears both in SUNDAY and MONDAY?

Moderate 03 Mark

The figure shows a circle of radius 9 cm with O as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ.

Moderate 03 Mark

In the given diagram, an isosceles △ABC is inscribed in a circle with centre O. PQ is a tangent to the circle at C. OM is perpendicular to chord AC and ∠COM = 65°. Find: (a) ∠ABC (b) ∠BAC (c) ∠BCQ

Moderate 03 Mark