If P = 2 6 3 9 and Q = 3 x y 2 , find x , y such that P Q = O .

Given, P = 2 6 3 9 , Q = 3 x y 2 We know that, PQ = O 2 6 3 9 × 3 x y 2 = 0 0 0 0 2 × 3 + 6 × y 2 × x + 6 × 2 3 × 3 + 9 × y 3 × x + 9 × 2 = 0 0 0 0 6 + 6 y 2 x + 12 9 + 9 y 3 x + 18 = 0 0 0 0 If A and B are two equal matrices, then a i j = b i j for all values of i and j . By the definition of equality of matrices, we have 6 + 6 y = 0 6 y = - 6 ⇒ y = - 1 Also, 2 x + 12 = 0 2 x = - 12 ⇒ x = - 6 ∴ x = - 6 , y = - 1

Let M × 1 1 0 2 = 1 2 where M is a matrix. State the order of the matrix M .

Given, Let M = a b M × 1 1 0 2 = 1 2 a b × 1 1 0 2 = 1 2 a + 0 a + 2 b = 1 2 The corresponding elements, We get, a = 1 and a + 2 b = 2 2 b = 2 - 1 = 1 b = 1 2 M = a b = 1 1 2 The order of matrix M be a × b M a × b × 1 1 0 2 2 × 2 = 1 2 1 × 2 Hence, the order of matrix M is 1 × 2 .

Let M × 1 1 0 2 = 1 2 where M is a matrix. Find the matrix M .

Given, Let M = a b M × 1 1 0 2 = 1 2 a b × 1 1 0 2 = 1 2 a + 0 a + 2 b = 1 2 The corresponding elements, We get, a = 1 and a + 2 b = 2 2 b = 2 - 1 = 1 b = 1 2 M = a b = 1 1 2 So, matrix M = 1 1 2 Hence, the required answer is as shown above.

Solve the matrix equation 4 1 X = - 4 8 - 1 2 .

Given, Let 4 1 X = - 4 8 - 1 2 We have, A X = B Order of matrix A = 2 × 1 Order of matrix B = 2 × 2 The product of A X should be 2 × 2 . So, order of X = 1 × 2 Let X = a b 4 1 a b = - 4 8 - 1 2 4 a 4 b a b = - 4 8 - 1 2 Equation the corresponding element we have 4 a = - 4 ⇒ a = - 1 4 b = 8 ⇒ b = 2 Hence, matrix X = - 1 2

If A = 2 - 1 - 4 5 and B = - 3 2 , find matrix C such that A C = B .

Given, A = 2 - 1 - 4 5 , B = - 3 2 Let the matrix C = x y We have, A C = B 2 - 1 - 4 5 x y = - 3 2 2 x - y - 4 x + 5 y = - 3 2 Equating two matrices, we get 2 x - y = - 3 - - - - - - ( i ) - 4 x + 5 y = 2 - - - - - ( i i ) Multiply by 2 in both sides in equation ( i ) 4 x - 2 y = - 6 - - - - - - ( i i i ) Subtract equation ( i i i ) and ( i i ) , we get 4 x - 2 y = - 6 - 4 x + 5 y = 2 3 y = - 4 ⇒ y = - 4 3 Substitute the value of y = - 4 3 in equation ( i ) , we get 2 x - y = - 3 2 x + 4 3 = - 3 6 x + 4 3 = - 3 ⇒ 6 x + 4 = - 9 6 x = - 9 - 4 ⇒ 6 x = - 13 x = - 13 6 Hence, the matrix C = - 13 6 - 4 3 .

If A = 2 - 1 - 4 5 and B = 0 - 3 , find a matrix C such that C A = B .

Given, A = 2 - 1 - 4 5 , B = 0 - 3 Let take the matrix C = x y Since the order of matrix A is 2 × 2 , and B = 1 × 2 Now, C A = B ⇒ x y 2 - 1 - 4 5 = 0 - 3 ⇒ 2 x - 4 y - x + 5 y = 0 - 3 On comparing, we get, 2 x - 4 y = 0 - - - - ( i ) - x + 5 y = - 3 - - - - ( i i ) 2 x - 2 y = 0 ⇒ x = 2 y Substitute x = 2 y in equation ( i i ) , we get - 2 y + 5 y = - 3 3 y = - 3 y = - 1 Substitute y = - 1 in equation ( i i ) , we get - x + 5 ( - 1 ) = - 3 - x - 5 = - 3 - x = - 3 + 5 x = - 2 Hence, the matrix C = - 2 - 1 .

If B = - 4 2 5 - 1 and C = 17 - 1 47 - 13 , find matrix A such that AB = C .

Given that, B = - 4 2 5 - 1 , C = 17 - 1 47 - 13 To find: matrix A such that AB = C Let A = p q r s Now, AB = C p q r s - 4 2 5 - 1 = 17 - 1 47 - 13 ⇒ - 4 p + 5 q 2 p - q - 4 r + 5 s 2 r - s = 17 - 1 47 - 13 If A and B are two equal matrices, then a i j = b i j for all values of i and j . On comparing we get, the equations - 4 p + 5 q = 17 - - - - ( i ) 2 p - q = - 1 - - - - ( i i ) - 4 r + 5 s = 47 - - - - ( i i i ) 2 r - s = - 13 - - - - ( i v ) Multiply 2 on both sides in equation ( i i ) , we get 4 p - 2 q = - 2 - - - - ( v ) Subtract equation ( v ) and equation ( i ) , 4 p - 2 q = - 2 - 4 p + 5 q = 17 3 q = 15 ∵ q = 15 3 = 5 Substitute the value of q in equation ( i i ) , 2 p - 5 = - 1 2 p = - 1 + 5 2 p = 4 p = 2 Multiply 2 on both sides in equation ( i v ) , we get 4 r - 2 s = - 26 - - - - - ( v i ) Now, we subtract equation ( v i ) and equation ( i i i ) , - 4 r + 5 s = 47 4 r - 2 s = - 26 3 s = 21 ∵ s = 21 3 = 7 Substitute the value of s in equation ( i v ) , 2 r - 7 = - 13 2 r = - 13 + 7 2 r = - 6 r = - 3 Hence, the matrix A = 2 5 - 3 7 .

E M B I B E

Understanding ICSE Mathematics Class 10>Algebra>Chapter 8 - Matrices>Exercise 8.3

M L Aggarwal Solutions for Exercise 3: Exercise 8.3

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 3: Exercise 8.3

Attempt the practice questions from Exercise 3: Exercise 8.3 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 3: Exercise 8.3 with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 18

If $A = [\begin{array}{l} 1 & 1 \\ x & x \end{array}]$ , find the value of $x$ so that $A^{2} = O$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 29

If $P = [\begin{array}{l} 2 & 6 \\ 3 & 9 \end{array}]$ and $Q = [\begin{array}{l} 3 & x \\ y & 2 \end{array}]$ , find $x, y$ such that $P Q = O$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 30

Let $M \times [\begin{array}{l} 1 & 1 \\ 0 & 2 \end{array}] = [\begin{matrix} 1 & 2 \end{matrix}]$ where $M$ is a matrix.

State the order of the matrix $M$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 30

Let $M \times [\begin{array}{l} 1 & 1 \\ 0 & 2 \end{array}] = [\begin{matrix} 1 & 2 \end{matrix}]$ where $M$ is a matrix.

Find the matrix $M$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 32

Solve the matrix equation $[\begin{array}{l} 4 \\ 1 \end{array}] X = [\begin{array}{l} - 4 & 8 \\ - 1 & 2 \end{array}]$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 33

If $A = [\begin{array}{r} 2 & - 1 \\ - 4 & 5 \end{array}]$ and $B = [\begin{array}{r} - 3 \\ 2 \end{array}]$ , find matrix $C$ such that $A C = B$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 33

If $A = [\begin{array}{r} 2 & - 1 \\ - 4 & 5 \end{array}]$ and $B = [\begin{matrix} 0 & - 3 \end{matrix}]$ , find a matrix $C$ such that $C A = B$ .

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 8 - Matrices>Exercise 8.3>Q 36

If $B = [\begin{matrix} - 4 & 2 \\ 5 & - 1 \end{matrix}]$ and $C = [\begin{matrix} 17 & - 1 \\ 47 & - 13 \end{matrix}]$ , find matrix $A$ such that $AB = C$ .

Learn and Prepare for any exam you want !

|

|

|

|

|

|

|

|