Given that M = 2 0 1 2 and N = 2 0 - 1 2 find M + 2 N .

Given, M = 2 0 1 2 N = 2 0 - 1 2 , Now we have to find M + 2 N M + 2 N = 2 0 1 2 + 2 2 0 - 1 2 On simplifying we get, = 2 0 1 2 + 4 0 - 2 4 = 2 + 4 0 + 0 1 - 2 2 + 4 = 6 0 - 1 6

If A = 2 0 - 3 1 and B = 0 1 - 2 3 find the value of 2 A - 3 B .

Given A = 2 0 - 3 1 B = 0 1 - 2 3 Now we have to find, ∴ 2 A - 3 B = 2 2 0 - 3 1 - 3 0 1 - 2 3 On simplifying we get = 4 0 - 6 2 - 0 3 - 6 9 = 4 - 0 0 - 3 - 6 6 2 - 9 = 4 - 3 0 - 7

Simplify: sin A sin A - cos A cos A sin A + cos A cos A sin A - sin A cos A

Given: sin A sin A - cos A cos A sin A + cos A cos A sin A - sin A cos A Multiplying the term outside with each term of the matrices, we get: ⇒ sin 2 A - sin A cos A sinA cos A sin 2 A + cos 2 A cos A sin A - cos A sin A cos 2 A Now, adding the matrices, we get: ⇒ sin 2 A + cos 2 A 0 0 sin 2 A + cos 2 A ⇒ 1 0 0 1 Hence, sin A sin A - cos A cos A sin A + cos A cos A sin A - sin A cos A = 1 0 0 1 .

If A = 0 - 1 1 2 and B = 1 2 - 1 1 find the matrix X if 3 A + X = B .

Given A = 0 - 1 1 2 B = 1 2 - 1 1 , Now we have to find 3 A + X = B X = B - 3 A Substituting the values we get X = 1 2 - 1 1 - 3 0 - 1 1 2 = 1 2 - 1 1 - 0 - 3 3 6 = 1 - 0 2 + 3 - 1 - 3 1 - 6 = 1 5 - 4 - 5

If A = 0 - 1 1 2 and B = 1 2 - 1 1 find the matrix X if X - 3 B = 2 A .

X - 3 B = 2 A X = 2 A + 3 B Now substituting the values A and B we get X = 2 0 - 1 1 2 + 3 1 2 - 1 1 = 0 - 2 2 4 + 3 6 - 3 3 = 0 + 3 - 2 + 6 2 - 3 4 + 3 = 3 4 - 1 7

If 2 × 3 4 5 x + 1 y 0 1 = z 0 10 5 , find the values of x , y and z .

2 × 3 4 5 x + 1 y 0 1 = z 0 10 5 6 8 10 2 x + 1 y 0 1 = z 0 10 5 6 + 1 8 + y 10 + 0 2 x + 1 = z 0 10 5 7 8 + y 10 2 x + 1 = z 0 10 5 By the definition of equality of matrices, we have ⇒ z = 7 2 x + 1 = 5 2 x = 4 ⇒ x = 2 Also, 8 + y = 0 ⇒ y = - 8 ∴ x = 2 , y = - 8 and z = 7

If 5 2 - 1 y + 1 - 2 × 1 2 x - 1 3 - 2 = 3 - 8 - 7 2 , find the values of x and y .

5 2 - 1 y + 1 - 2 × 1 2 x - 1 3 - 2 = 3 - 8 - 7 2 5 2 - 1 y + 1 - 2 4 x - 2 6 - 4 = 3 - 8 - 7 2 5 - 2 2 - ( 4 x - 2 ) ( - 1 ) - 6 y + 1 - ( - 4 ) = 3 - 8 - 7 2 3 4 - 4 x - 7 y + 5 = 3 - 8 - 7 2 By the definition of equality of matrices, we have 4 - 4 x = - 8 ⇒ 4 x = 12 ⇒ x = 3 Also, y + 5 = 2 ⇒ y = - 3 ∴ x = 3 and y = - 3

If A = 2 a - 3 5 , B = - 2 3 7 b , C = c 9 - 1 - 11 and 5 A + 2 B = C , find the values of a , b and c .

A = 2 a - 3 5 , B = - 2 3 7 b , C = c 9 - 1 - 11 5 A + 2 B = C 5 × 2 a - 3 5 + 2 × - 2 3 7 b = c 9 - 1 - 11 10 5 a - 15 25 + - 4 6 14 2 b = c 9 - 1 - 11 10 + ( - 4 ) 5 a + 6 ( - 15 ) + 14 25 + 2 b = c 9 - 1 - 11 6 5 a + 6 - 1 25 + 2 b = c 9 - 1 - 11 By the definition of equality of matrices, we have ⇒ c = 6 Also, 5 a + 6 = 9 5 a = 3 ⇒ a = 3 5 Also, 25 + 2 b = - 11 2 b = - 36 ⇒ b = - 18

E M B I B E

Understanding ICSE Mathematics Class 10>Algebra>Chapter 8 - Matrices>Exercise 8.2

M L Aggarwal Solutions for Exercise 2: Exercise 8.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 2: Exercise 8.2

Attempt the practice questions from Exercise 2: Exercise 8.2 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Exercise 2: Exercise 8.2 with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 1

Given that $M = [\begin{matrix} 2 & 0 \\ 1 & 2 \end{matrix}]$ and $N = [\begin{matrix} 2 & 0 \\ - 1 & 2 \end{matrix}]$ find $M + 2 N$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 2

If $A = [\begin{matrix} 2 & 0 \\ - 3 & 1 \end{matrix}]$ and $B = [\begin{matrix} 0 & 1 \\ - 2 & 3 \end{matrix}]$ find the value of $2 A - 3 B$ .

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 3

Simplify:

$\sin A [\begin{matrix} \sin A & - \cos A \\ \cos A & \sin A \end{matrix}] + \cos A [\begin{matrix} \cos A & \sin A \\ - \sin A & \cos A \end{matrix}]$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 5

If $A = [\begin{matrix} 0 & - 1 \\ 1 & 2 \end{matrix}] and B = [\begin{matrix} 1 & 2 \\ - 1 & 1 \end{matrix}]$ find the matrix $X$ if $3 A + X = B$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 5

If $A = [\begin{matrix} 0 & - 1 \\ 1 & 2 \end{matrix}] and B = [\begin{matrix} 1 & 2 \\ - 1 & 1 \end{matrix}]$ find the matrix $X$ if $X - 3 B = 2 A$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 11

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

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 12

If $[\begin{matrix} 5 & 2 \\ - 1 & y + 1 \end{matrix}] - 2 \times [\begin{matrix} 1 & 2 x - 1 \\ 3 & - 2 \end{matrix}] = [\begin{matrix} 3 & - 8 \\ - 7 & 2 \end{matrix}]$ , find the values of $x$ and $y$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.2>Q 14

If $A = [\begin{matrix} 2 & a \\ - 3 & 5 \end{matrix}]$ , $B = [\begin{matrix} - 2 & 3 \\ 7 & b \end{matrix}]$ , $C = [\begin{matrix} c & 9 \\ - 1 & - 11 \end{matrix}]$ and $5 A + 2 B = C$ , find the values of $a$ , $b$ and $c$ .

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