Construct a 1 × 3 order matrix, whose elements are given by c i j = 4 i - 3 j .

Given, To construct a matrix of 1 × 3 , whose elements are given by c i j = 4 i - 3 j To form a matrix, whose elements satisfies this relation, we put different values of i and j according to the given order and find all the elements of matrix and then write the matrix of given order. Let C be the matrix of order 1 × 3 So, C = c i j 1 × 3 = c 11 c 12 c 13 We have c i j = 4 i - 3 j ........ i On putting values i = 1 and j = 1 , 2 , 3 in equation 1 , we get c 11 = 4 1 - 3 1 = 1 c 12 = 4 1 - 3 2 = - 2 c 13 = 4 1 - 3 3 = - 5 Therefore, we get C = 1 - 2 - 5 Hence, the above is the required matrix.

Construct a 3 × 3 order matrix, whose elements are given by a i j = sin i x cos e c j x .

Given, To construct a matrix of 3 × 3 , whose elements are given by a i j = sin i x cos e c j x To form a matrix, whose elements satisfies this relation, we put different values of i and j according to the given order and find all the elements of matrix and then write the matrix of given order. Let A be the matrix of order 3 × 3 So, A = a i j 3 × 3 = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 We have a i j = sin i x cos e c j x ........ i On putting values i = 1 , 2 , 3 and j = 1 , 2 , 3 in equation i , we get Therefore, we get a 11 = sin 1 x cos e c 1 x = 1 a 12 = sin 1 x cos e c 2 x = sin x cos e c 2 x a 13 = sin 1 x cos e c 3 x = sin x cos e c 3 x a 21 = sin 2 x cos e c 1 x = sin 2 x cos e c x a 22 = sin 2 x cos e c 2 x = 1 a 23 = sin 2 x cos e c 3 x = sin 2 x cos e c 3 x a 31 = sin 3 x cos e c 1 x = sin 3 x cos e c x a 32 = sin 3 x cos e c 2 x = sin 3 x cos e c 2 x a 33 = sin 3 x cos e c 3 x = 1 Therefore, we get 1 sin x cos e c 2 x sin x cos e c 3 x sin 2 x cos e c x 1 sin 2 x cos e c 3 x sin 3 x cos e c x sin 3 x cos e c 2 x 1 Hence, the above is the required matrix.

Find the values of a , b , c and d , if a - 2 b 7 = 2 c 3 2 c + d

Given, To find values of a , b , c and d a - 2 b 7 = 2 c 3 2 c + d Here, both matrices are equal, so to find a , b , c and d , we equate the corresponding elements. On equating the corresponding elements, we get a = 2 - 2 = c ...... i b = 3 7 = 2 c + d Putting value of c from equation i we get 7 = 2 × - 2 + d d = 7 + 4 = 11 Hence, a = 1 , b = 3 , c = - 2 and d = 11 .

Find the values of a , b , c and d , if a + b 3 4 c = 2 d b 1

Given, To find values of a , b , c and d a + b 3 4 c = 2 d b 1 Here, both matrices are equal, so to find a , b , c and d , we equate the corresponding elements. On equating the corresponding elements, we get a + b = 2 ...... i i 3 = d b = 4 ...... i c = 1 Putting value of b from equation i into equation i i , we get a + b = 2 a + 4 = 2 a = - 2 Hence, a = - 2 , b = 4 , c = 1 and d = 3 .

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

Given, To find values of x , y , a and b x + y a - a + b 2 x - 3 y = 5 3 - 1 - 5 Here, both matrices are equal, so to find x , y , a and b , we equate the corresponding elements. On equating the corresponding elements, we get x + y = 5 ........... i a - b = 3 ........... i i a + b = - 1 ....... i i i 2 x - 3 y = - 5 ....... i v On solving equation i i and i i i we get a = 1 , b = - 2 On solving equation i and i v we get x = 2 , y = 3 Hence, a = 1 , b = - 2 , x = 2 and y = 3 .

E M B I B E

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 5

MEDIUM

10th ICSE

IMPORTANT

Earn 100

If a matrix has $32$ elements, then what are the possible orders it can have?

Important Questions on Matrices

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 6

If a matrix has

40

elements, then what are the possible orders it can have? What, if it has

41

elements ?

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 7

Construct a

1 \times 3

order matrix, whose elements are given by

c_{i j} = 4 i - 3 j

.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 8

Construct a

3 \times 3

order matrix, whose elements are given by

a_{i j} = \sin i x \cos e c j x

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 9

Find the values of $a, b, c$ and $d$ , if

$[\begin{matrix} a & - 2 \\ b & 7 \end{matrix}] = [\begin{matrix} 2 & c \\ 3 & 2 c + d \end{matrix}]$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 10

Find the values of $a, b, c$ and $d$ , if

$[\begin{matrix} a + b & 3 \\ 4 & c \end{matrix}] = [\begin{matrix} 2 & d \\ b & 1 \end{matrix}]$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 11

If

[\begin{matrix} x - 3 & x - z - 4 \\ z & x + y + z \end{matrix}] = I

, where

I

is the identity matrix of same order, then find the values of

x, y

and

z

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 12

Find the values of $x, y, a$ and $b$ , when

$[\begin{matrix} x + y & a - \\ a + b & 2 x - 3 y \end{matrix}] = [\begin{matrix} 5 & 3 \\ - 1 & - 5 \end{matrix}]$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 8 - Matrices>CHAPTER EXERCISE>Q 13

If $[\begin{matrix} 39 & 5 x + 7 y \\ 2 x - 5 y & 41 \end{matrix}] = [\begin{matrix} 7 u + 9 v & 1 \\ 16 & 9 u + 7 \end{matrix}]$ , then find the value of $x + y + u + v$ .