If A = 2 - 2 4 2 - 5 1 , B = 8 0 4 - 2 3 6 , find matrix X such that 2 A + 3 X = 5 B .

Given that A = 2 - 2 4 2 - 5 1 , B = 8 0 4 - 2 3 6 2 A = 2 2 - 2 4 2 - 5 1 = 4 - 4 8 4 - 10 2 5 B = 5 8 0 4 - 2 3 6 = 40 0 20 - 10 15 30 Now, 2 A + 3 X = 5 B ⇒ 4 - 4 8 4 - 10 2 + 3 X = 40 0 20 - 10 15 30 ⇒ 3 X = 40 0 20 - 10 15 30 - 4 - 4 8 4 - 10 2 ⇒ 3 X = 40 - 4 0 + 4 20 - 8 - 10 - 4 15 + 10 30 - 2 ⇒ 3 X = 36 4 12 - 14 25 28 ⇒ X = 1 3 36 4 12 - 14 25 28 ⇒ X = 12 4 3 4 - 14 3 25 3 28 3

If 2 3 4 5 x + 1 y 0 1 = 7 0 10 5 , find x and y .

Given, 2 3 4 5 x + 1 y 0 1 = 7 0 10 5 ⇒ 6 8 10 2 x + 1 y 0 1 = 7 0 10 5 ⇒ 6 + 1 8 + y 10 + 0 2 x + 1 = 7 0 10 5 If two matrices are equal, then their corresponding elements are equal. ∴ 8 + y = 0 ⇒ y = − 8 And 2 x + 1 = 5 ⇒ x = 4 2 = 2 ∴ x = 2 and y = − 8

Find a matrix X such that 2 A + B + X = O , where A = - 1 2 3 4 , B = 3 - 2 1 5

Given matrices are A = - 1 2 3 4 , B = 3 - 2 1 5 Order of the matrices A & B is 2 × 2 . So, the null matrix O is given by 0 0 0 0 2 A = 2 - 1 2 3 4 = - 2 4 6 8 Now 2 A + B + X = O ⇒ - 2 4 6 8 + 3 - 2 1 5 + X = 0 0 0 0 ⇒ - 2 + 3 4 - 2 6 + 1 8 + 15 + X = 0 0 0 0 ⇒ 1 2 7 13 + X = 0 0 0 0 ⇒ X = 0 0 0 0 - 1 2 7 13 ∴ X = - 1 - 2 - 7 - 13

If A = 8 0 4 - 2 3 6 and B = 2 - 2 4 2 - 5 1 , then find the matrix X of order 3 × 2 such that 2 A + 3 X = 5 B .

Given that A = 8 0 4 - 2 3 6 and B = 2 - 2 4 2 - 5 1 2 A = 2 8 0 4 - 2 3 6 = 16 0 8 - 4 6 12 5 B = 5 2 - 2 4 2 - 5 1 = 10 - 10 20 10 - 25 5 Now, 2 A + 3 X = 5 B ⇒ 16 0 8 - 4 6 12 + 3 X = 10 - 10 20 10 - 25 5 ⇒ 3 X = 10 - 10 20 10 - 25 5 - 16 0 8 - 4 6 12 ⇒ 3 X = 10 - 16 - 10 - 0 20 - 8 10 + 4 - 25 - 6 5 - 12 ⇒ 3 X = - 6 - 10 12 14 - 31 - 7 ⇒ X = 1 3 - 6 - 10 12 14 - 31 - 7 ∴ X = - 2 - 10 3 12 14 3 - 31 3 - 7 3

Find x , y , z and t , if 3 x y z t = x 6 - 1 2 t + 4 x + y z + t 3

Given that 3 x y z t = x 6 - 1 2 t + 4 x + y z + t 3 ⇒ 3 x 3 y 3 z 3 t = x + 4 6 + x + y - 1 + z + t 2 t + 3 If two matrices are equal, then their corresponding elements are equal. ∴ 3 x = x + 4 ⇒ x = 2 Also, 3 y = 6 + x + y ⇒ 2 y = 6 + x ⇒ 2 y = 8 ∵ x = 2 ⇒ y = 4 Now, 3 t = 2 t + 3 ⇒ t = 3 And 3 z = − 1 + z + t ⇒ 2 z = − 1 + t 2 z = − 1 + 3 ⇒ z = 1 ∴ x = 2 , y = 4 , z = 1 and t = 3

E M B I B E

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE

R D Sharma Solutions for Chapter: Algebra of Matrices, Exercise 1: EXERCISE

Author:R D Sharma

R D Sharma Mathematics Solutions for Exercise - R D Sharma Solutions for Chapter: Algebra of Matrices, Exercise 1: EXERCISE

Attempt the free practice questions on Chapter 5: Algebra of Matrices, Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. MATHEMATICS CLASS XII VOLUME-1 solutions are prepared by Experienced Embibe Experts.

Questions from R D Sharma Solutions for Chapter: Algebra of Matrices, Exercise 1: EXERCISE with Hints & Solutions

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 13

If $A = [\begin{matrix} 2 & - 2 \\ 4 & 2 \\ - 5 & 1 \end{matrix}], B = [\begin{matrix} 8 & 0 \\ 4 & - 2 \\ 3 & 6 \end{matrix}]$ , find matrix $X$ such that $2 A + 3 X = 5 B$ .

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 16

If $2 [\begin{matrix} 3 & 4 \\ 5 & x \end{matrix}] + [\begin{matrix} 1 & y \\ 0 & 1 \end{matrix}] = [\begin{matrix} 7 & 0 \\ 10 & 5 \end{matrix}]$ , find $x$ and $y$ .

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 17

Find the value of $λ$ , a non-zero scalar, if $λ [\begin{matrix} 1 & 0 & 2 \\ 3 & 4 & 5 \end{matrix}] + 2 [\begin{matrix} 1 & 2 & 3 \\ - 1 & - 3 & 2 \end{matrix}] = [\begin{matrix} 4 & 4 & 10 \\ 4 & 2 & 14 \end{matrix}]$ .

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 18

Find a matrix $X$ such that $2 A + B + X = O$ , where $A = [\begin{matrix} - 1 & 2 \\ 3 & 4 \end{matrix}], B = [\begin{matrix} 3 & - 2 \\ 1 & 5 \end{matrix}]$

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 18

If $A = [\begin{matrix} 8 & 0 \\ 4 & - 2 \\ 3 & 6 \end{matrix}]$ and $B = [\begin{matrix} 2 & - 2 \\ 4 & 2 \\ - 5 & 1 \end{matrix}]$ , then find the matrix $X$ of order $3 \times 2$ such that $2 A + 3 X = 5 B$ .

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 19

Find $x, y, z$ and $t$ , if

$3 [\begin{matrix} x & y \\ z & t \end{matrix}] = [\begin{matrix} x & 6 \\ - 1 & 2 t \end{matrix}] + [\begin{matrix} 4 & x + y \\ z + t & 3 \end{matrix}]$

EASY

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 20

If $X$ and $Y$ are $2 \times 2$ matrices, then solve the following matrix equations for $X$ and $Y$ .

$2 X + 3 Y = [\begin{matrix} 2 & 3 \\ 4 & 0 \end{matrix}], 3 X + 2 Y = [\begin{matrix} - 2 & 2 \\ 1 & - 5 \end{matrix}]$

MEDIUM

12th CBSE

IMPORTANT

MATHEMATICS CLASS XII VOLUME-1>Chapter 5 - Algebra of Matrices>EXERCISE>Q 22

The monthly incomes of Aryan and Babban are in the ratio $3 : 4$ and their monthly expenditures are in the ratio $5 : 7$ . If each saves $Rs 15, 000$ per month, find their monthly incomes using matrix method. This problem reflects which value?

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