Construct a 2 × 2 matrix whose elements a i j are given by a i j = 2 i - j

Given that A = a i j 2 × 2 So, the 2 × 2 matrix is given by a 11 a 12 a 21 a 23 Now, a i j = 2 i - j ⇒a 11 = 2 ( 1 ) - 1 = 2 - 1 = 1 , ⇒a 12 = 2 ( 1 ) - 2 = 2 - 2 = 0 , ⇒a 21 = 2 ( 2 ) - 1 = 4 - 1 = 3 , ⇒a 22 = 2 ( 2 ) - 2 = 4 - 2 = 2 , Hence, the required matrix 1 0 3 2

Construct a 2 × 2 matrix, whose elements are given by a i j = i . j .

Given, to construct a matrix 2 × 2 where the elements are given as a i j = i . j Let the matrix be A = a 11 a 12 a 21 a 22 its elements will be a 11 = 1 . 1 = 1 a 12 = 1 . 2 = 2 a 21 = 2 . 1 = 2 a 22 = 2 . 2 = 4 Hence, the matrix will be A = 1 2 2 4

Find the values of x and y if 2 x + y 3 x - 2 y = 5 4

2 x + y 3 x - 2 y = 5 4 By the definition of equality of matrices, we get 2 x + y = 5 ...... ( i ) 3 x - 2 y = 4 .......... ( ii ) Multiplying equation ( i ) by 3 and equation ( ii ) by 2 , we get 6 x + 3 y = 15 ..... ( iii ) 6 x - 4 y = 8 ........ ( iv ) Subtracting equation ( iv ) from equation ( iii ) , we get 8 y = 7 ⇒ y = 7 8 ..... ( v ) Putting the value of y from equation ( v ) in the equation ( i ) , we get 2 x + 7 8 = 5 2 x = 5 - 7 8 = 33 8 ⇒ x = 33 16 ∴ x = 33 16 , y = 7 8

If x + 3 4 y - 4 x + y = 5 4 3 9 , find the values of x and y .

x + 3 4 y - 4 x + y = 5 4 3 9 By the definition of equality of matrices, we have x + 3 = 5 ⇒ x = 2 Also, y - 4 = 3 ⇒ y = 7 ∴ x = 2 , y = 7

Find the values of x , y , a and b if x - 2 y a + 2 b 3 a - b = 3 1 5 1

x - 2 y a + 2 b 3 a - b = 3 1 5 1 By the definition of equality of matrices, we have x - 2 = 3 ⇒ x = 5 Also, ⇒ y = 1 Also, a + 2 b = 5 ...... ( i ) and 3 a - b = 1 ....... ( ii ) Multiplying equation ( i ) by 3 , we get 3 a + 6 b = 15 ..... ( iii ) Subtracting equation ( ii ) from equation ( iii ) , we get 7 b = 14 ⇒ b = 2 ...... ( iv ) Putting the value of b from equation ( iv ) in the equation ( i ) , we get a + 2 × 2 = 5 ⇒ a = 5 - 4 = 1 ∴ x = 5 , y = 1 , a = 1 and b = 2

Find the values of a , b , c and d if a + b 3 5 + c a b = 6 d - 1 8

a + b 3 5 + c a b = 6 d - 1 8 By the definition of equality of matrices, we have ⇒ d = 3 Also, 5 + c = - 1 ⇒ c = - 6 Also, a + b = 6 ...... ( i ) and a b = 8 b = 8 a ...... ( ii ) Putting the value of b from equation ( ii ) in the equation ( i ) , we get a + 8 a = 6 a 2 + 8 a = 6 a 2 - 6 a + 8 = 0 ( a - 4 ) ( a - 2 ) = 0 ⇒ a = 4 , or a = 2 When a = 4 : b = 8 4 = 2 (from equation ( ii ) ) When a = 2 : b = 8 2 = 4 (from equation ( ii ) ) ∴ a = 4 , b = 2 , c = - 6 and d = 3 OR a = 2 , b = 4 , c = - 6 and d = 3

E M B I B E

Understanding ICSE Mathematics Class 10>Algebra>Chapter 8 - Matrices>Exercise 8.1

M L Aggarwal Solutions for Exercise 1: Exercise 8.1

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 1: Exercise 8.1

Attempt the practice questions from Exercise 1: Exercise 8.1 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 1: Exercise 8.1 with Hints & Solutions

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 2

If a matrix has $4$ elements, what are the possible orders it can have?

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 3

If a matrix has $8$ elements, what are the possible orders it can have?

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 3

Construct a $2 \times 2$ matrix whose elements $a_{i j}$ are given by

$a_{i j} = 2 i - j$

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 4

Construct a $2 \times 2$ matrix, whose elements are given by $a_{i j} = i . j$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 5

Find the values of $x$ and $y$ if $[\begin{matrix} 2 x + y \\ 3 x - 2 y \end{matrix}] = [\begin{matrix} 5 \\ 4 \end{matrix}]$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 7

If $[\begin{matrix} x + 3 & 4 \\ y - 4 & x + y \end{matrix}] = [\begin{matrix} 5 & 4 \\ 3 & 9 \end{matrix}]$ , find the values of $x$ and $y$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 8

Find the values of $x$ , $y$ , $a$ and $b$ if $[\begin{matrix} x - 2 & y \\ a + 2 b & 3 a - b \end{matrix}] = [\begin{matrix} 3 & 1 \\ 5 & 1 \end{matrix}]$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.1>Q 9

Find the values of $a$ , $b$ , $c$ and $d$ if $[\begin{matrix} a + b & 3 \\ 5 + c & a b \end{matrix}] = [\begin{matrix} 6 & d \\ - 1 & 8 \end{matrix}]$

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