CHAPTER NAME- MATRICES
Concise Mathematics Class 10 ICSE Solutions
Solutions of chapter 9 Exercise. 9(D)
Question 1.Find x and y, if:
Solution:
Comparing the corresponding elements, we get,
6x - 10 = 8
6x = 18
x=3
-2x + 14 = 4y
4y = -6+ 14 = 8
y=2
Question 2.Find x and y, if:
Solution:
Comparing the corresponding elements, we get,
3x + 18 = 15
3x = -3
x = -1
12x + 77 = 10y
10y = -12 + 77 = 65
y = 6.5
Question 3.
If ; find x and y, if:
(i) x, y i W (whole numbers)
(ii) x, y I Z (integers)
Solution:
2
(i) x, y i W (whole numbers)
It can be observed that the above two equations are satisfied when x = 3
and y = 4.
(ii) x, y i Z (integers)
It can be observed that the above two equations are satisfied when x =
3 and y = 4.
Question 4.
Solution:
(i)
(ii)
3
Question 5.Evaluate:
Solution:
Question 6.
If and 3A x M = 2B; find matrix M.
Solution:
Let the order of matrix M be a x b.
4
3A x M = 2B
Clearly, the order of matrix M is 2 x 1.
Comparing the corresponding elements, we get,
-3y = -10
y=
12x - 9y = 12
5
Question 7.
If , find the values of a, b and c.
Solution:
Comparing the corresponding elements, we get,
a+1=5 a=4
2+b=0 b = -2
-1 - c = 3 c = -4
Question 8.
If A = ; find:
(i) A (BA)
(ii) (AB). B
Solution:
(i)
6
(ii)
Question 9.Find x and y, if:
Solution:
7
Comparing the corresponding elements, we get,
5x = 5 x=1
6y = 12 y=2
Question 10.If matrix X = and 2X - 3Y = ; find the
matrix 'X' and 'Y'.
Solution:
8
Question 11.Given ; find the matrix X
such that:
A + X = 2B + C
Solution:
Given, A + X = 2B + C
9
Question 12.Find the value of x, given that A2 = B,
Solution:
Given, A2 = B
Comparing the corresponding elements, we get,
x = 36
Question 13.
If , and I is identity matrix of the same order
and At is the transpose of matrix A, find At .B + BI
10
Solution:
Question 14.
Solution:
11
Question 15.
Let . Find A2 - A + BC.
Solution:
Question 16.
12
Let A = . Find A2 + AB + B2.
Solution:
A=
A2 = A A=
AB = A B=
B2 = B x B =
A2 + AB + B2 =
13
=
Question 17.
If and 3A - 2C = 6B, find the values of a,
b and c.
Solution:
Comparing the corresponding elements, we get,
3a - 8 = 24 3a = 32 a=
24 - 2b = 0 2b = 24 b = 12
11 = 6c c=
Question 18.
Given A = .
Find the values of p and q.
Solution:
14
A=
BA =
C2 =
BA = C2 =
By comparing,
-2q = -8 q=4
And p = 8
Question 19.
Given A = . Find AB + 2C - 4D.
Solution:
AB =
Question 20.Evaluate:
Solution:
15
=
Question 21.
Solution:
16
Question 22.
Solution:
A2 = 9A + MI
⇒ A2 - 9A = mI ….(1)
Now, A2 = AA
17
Substituting A2 in (1), we have
A2 - 9A = mI
Question 23.
(i) Write the order of matrix X.
(ii) Find the matrix 'X'
Solution:
(i) Let the order of matrix X = m × n
Order of matrix A = 2 × 2
Order of matrix B = 2 × 1
Now, AX = B
18
∴ m = 2 and n = 1
Thus, order of matrix X = m × n = 2 × 1
Multiplying (1) by 2, we get
4x + 2y = 8 ….(3)
Subtracting (2) from (3), we get
3x = 3
⇒x=1
Substituting the value of x in (1), we get
2(1) + y = 4
19
⇒2+y=4
⇒y=2
Question 24.
Find the matrix C where C
is a 2 by 2 matrix.
Solution:
Given: A2 - 5B2 = 5C
20
Question 25.Given matrix . Find the matrix X if, X = B2 - 4B.
Hence, solve for a and b given .
Solution:
To find: a and b
21
