If x - y z 2 x - y w = - 1 4 0 5 , find the value of x + y .

Given that, x - y z 2 x - y w = - 1 4 0 5 To find : value of x + y Now, x - y z 2 x - y w = - 1 4 0 5 Equating the corresponding elements... x - y = - 1 y = x + 1 . . . . . . . . 1 Put the value of y 2 x - y = 0 . . . . . . . 2 2 x - ( x + 1 ) = 0 2 x - x - 1 = 0 x - 1 = 0 x = 1 Put x in equation 1 y = x + 1 y = 1 + 1 y = 2 Hence, x + y = 1 + 2 = 3 .

If x + y x + 2 2 x - y 16 = 8 5 1 3 y + 1 , then write the value of y - x .

Given that, x + y x + 2 2 x - y 16 = 8 5 1 3 y + 1 To find : value of y - x Now, x + y x + 2 2 x - y 16 = 8 5 1 3 y + 1 Equate the corresponding elements... x + y = 8 x + 2 = 5 . . . . . . . . . . . . . 2 2 x - y = 1 3 y + 1 = 16 . . . . . . . . . . . 1 From equation 1 and 2 3 y + 1 = 16 x + 2 = 5 y = 15 x = 3 We have to find y - x From 3 y - x = 15 - 3 = 12 Hence, y - x = 12 .

Write the value of x - y + z from the following equations: x + y + z x + z y + z = 9 5 7

Given that, x + y + z x + z y + z = 9 5 7 To find : value of x - y + z Now, x + y + z x + z y + z = 9 5 7 Equate the corresponding elements.... x + y + z = 9 . . . . . . . . . . . . 1 x + z = 5 . . . . . . . . . . . . 2 y + z = 7 . . . . . . . . . . . 3 x = 5 - z [from equation 2 ] y = 7 - z [from equation 3 ] Put the value of x and y in equation 1 x + y + z = 9 5 - z + 7 - z + z = 9 12 - z = 9 z = 3 Put the value of z in equation 2 and 3 x + 3 = 5 x = 2 y + 3 = 7 y = 4 Hence, x - y + z = 2 - 4 + ( 3 ) = 1

If x 3 x - y 2 x + z 3 y - w = 3 2 4 7 , find x , y , z and w .

Given that, x 3 x - y 2 x + z 3 y - w = 3 2 4 7 To find : x , y , z and w Now, x 3 x - y 2 x + z 3 y - w = 3 2 4 7 Equate the corresponding elements... x = 3 . . . . . . . . . . . . . . 1 3 x - y = 2 . . . . . . . . . . . 2 ⇒ 9 - y = 2 ⇒ y = 9 - 2 = 7 And 2 x + z = 4 . . . . . . . . . . . . . 3 ⇒ 6 + z = 4 ⇒ z = 4 - 6 = - 2 Also, 3 y - w = 7 . . . . . . . . . . 4 ⇒ 3 × 7 - 7 = 14 Hence, x = 3 , y = 7 , z = 2 , w = 14 .

Find the values of a , b , c and d from the following equations: 2 a + b a - 2 b 5 c - d 4 c + 3 d = 4 - 3 11 24 .

Given that, 2 a + b a - 2 b 5 c - d 4 c + 3 d = 4 - 3 11 24 To find : value of a , b , c and d Now, 2 a + b a - 2 b 5 c - d 4 c + 3 d = 4 - 3 11 24 Equating the corresponding elements... 2 a + b = 4 ⇒ b = 4 - 2 a . . . . . . . . . . . 1 a - 2 b = - 3 . . . . . . . . . . . . . 2 ⇒ a - 2 4 - 2 a = - 3 [from (1)] ⇒ a - 8 + 4 a = - 3 ⇒ a = 1 Put the value of a in equation 1 b = 4 - 2 1 ⇒ b = 2 5 c - d = 11 ⇒ 5 c - 11 = d . . . . . . . . . . 3 4 c + 3 d = 24 . . . . . . . . . . . 4 ⇒ 4 c + 3 5 c - 11 = 24 [from (3)] ⇒ c = 3 Put the value of c in 3 5 × 3 - 11 = d ⇒ d = 4 . Hence, a = 1 , b = 2 , c = 3 , d = 4 .

Find x , y , a and b if 2 x - 3 y a - b 3 1 x + 4 y 3 a + 4 b = 1 - 2 3 1 6 29 .

Given that, 2 x - 3 y a - b 3 1 x + 4 y 3 a + 4 b = 1 - 2 3 1 6 29 To find : x , y , a and b Now, 2 x - 3 y a - b 3 1 x + 4 y 3 a + 4 b = 1 - 2 3 1 6 29 Equating the corresponding elements... 2 x - 3 y = 1 . . . . . . . . . . 1 ; a - b = - 2 . . . . . . . . . . 2 x + 4 y = 6 . . . . . . . . . . . . . 3 ; 3 a + 4 b = 29 . . . . . . . . . 4 Solving equation 1 and 3 using elimination method 2 x - 3 y = 1 2 x ± 8 y = ± 12 - 11 y = - 11 ¯ y = 1 Put in 1 ∴ 2 x - 3 1 = 1 2 x = 4 x = 2 Solving equation 2 and 4 using elimination method 3 a - 3 b = - 6 3 a ± 4 b = ± 29 - 7 b = - 35 ¯ b = 5 Put in 2 ∴ a - b = - 2 a = - 2 + 5 a = 3 Hence, x = 2 , y = 1 , a = 3 , b = 5 .

Write the number of all possible matrices of order 2 × 3 with each entry 1 or 2 ?

We know that if P = p i j n × m , then P is called n × m matrix and each row of P contains m elements and each column of P contains n elements and the total number of elements in the matrix P is equal to m n . Let A be a matrix of order 2 × 3 which has the entry 1 or 2 . So, the total number of elements in the matrix A is equal to 6 and all the elements of A are either 1 or 2 . Hence, the total number of matrix A is equal to 2 6 = 64 .

Write the number of all possible matrices of order 2 × 2 with each entry 1 , 2 or 3 ?

Given that, Matrices of order 2 × 2 with each entry 1 , 2 or 3 To find : all possible matrices Now, Order of matrix 2 × 2 [given] So number of elements will be 2 × 2 = 4 It is also given that each entry can be either 1 , 2 or 3 Hence, the number of possible matrices = 3 4 i.e. 3 × 3 × 3 × 3 = 81 Hence, possible matrices that can be formed is 81 .

E M B I B E

Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.1

M L Aggarwal Solutions for Chapter: Matrices, Exercise 1: EXERCISE 3.1

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Matrices, Exercise 1: EXERCISE 3.1

Attempt the practice questions on Chapter 3: Matrices, Exercise 1: EXERCISE 3.1 with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 12 Volume 1 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Matrices, Exercise 1: EXERCISE 3.1 with Hints & Solutions

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.1

If $[\begin{matrix} x - y & z \\ 2 x - y & w \end{matrix}] = [\begin{matrix} - 1 & 4 \\ 0 & 5 \end{matrix}]$ , find the value of $(x + y)$ .

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.1

If $[\begin{matrix} x + y & x + 2 \\ 2 x - y & 16 \end{matrix}] = [\begin{matrix} 8 & 5 \\ 1 & 3 y + 1 \end{matrix}]$ , then write the value of $(y - x)$ .

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.1

Write the value of $x - y + z$ from the following equations:

$[\begin{matrix} x + y + z \\ x + z \\ y + z \end{matrix}] = [\begin{matrix} 9 \\ 5 \\ 7 \end{matrix}]$

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.1

If $[\begin{matrix} x & 3 x - y \\ 2 x + z & 3 y - w \end{matrix}] = [\begin{matrix} 3 & 2 \\ 4 & 7 \end{matrix}]$ , find $x, y, z$ and $w$ .

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.1

Find the values of $a, b, c$ and $d$ from the following equations:

$[\begin{matrix} 2 a + b & a - 2 b \\ 5 c - d & 4 c + 3 d \end{matrix}] = [\begin{matrix} 4 & - 3 \\ 11 & 24 \end{matrix}]$ .

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.1

Find $x, y, a$ and $b$ if $[\begin{matrix} 2 x - 3 y & a - b & 3 \\ 1 & x + 4 y & 3 a + 4 b \end{matrix}] = [\begin{matrix} 1 & - 2 & 3 \\ 1 & 6 & 29 \end{matrix}]$ .