EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
3 ✕ 1 , 1 ✕ 3
(ii)
1 ✕ 2 , 2 ✕ 1
(iii)
2 ✕ 3 , 3 ✕ 1
(iv)
1 ✕ 2 , 2 ✕ 3
(v)
3 ✕ 2 , 1 ✕ 2
Question
2
2.
If A =
[
1
2
0
-2
]
, then find B satisfying A
+
B = I
(i)
[
-1
-2
0
3
]
(ii)
[
0
-2
3
3
]
(iii)
[
-2
-2
0
3
]
(iv)
[
0
-2
0
4
]
(v)
[
0
-2
0
3
]
Question
3
3.
If A =
[
3
0
0
x
]
is a scalar matrix, then x = ?
(i)
x
(ii)
3
(iii)
1
(iv)
0
(v)
9
Question
4
4.
If A =
[
-2
1
3
-2
1
2
-2
3
2
]
and B =
[
-1
-1
0
2
-2
-1
1
0
-1
]
, then A
✕
B =
(i)
[
10
0
-4
6
0
-3
10
-4
-5
]
(ii)
[
7
0
-4
6
0
-3
10
-4
-4
]
(iii)
[
7
0
-4
6
0
-3
10
-5
-5
]
(iv)
[
7
0
-4
6
0
-3
10
-4
-5
]
(v)
[
7
-2
-4
6
0
-3
10
-4
-5
]
Question
5
5.
If A =
[
0
-3
-6
6
]
, then find B satisfying A
+ B = O
(i)
[
0
3
6
-6
]
(ii)
[
0
4
6
-6
]
(iii)
[
0
3
6
-7
]
(iv)
[
0
3
4
-6
]
(v)
[
2
3
6
-6
]
Question
6
6.
Which of the following are true?
a)
A matrix is symmetric if the principal diagonal elements are same
b)
If a matrix is symmetric then it is equal to its transpose
c)
If a matrix is symmetric, then it is a square matrix
d)
A rectangular matrix cannot be symmetric
(i)
{a,d}
(ii)
{a,b,c}
(iii)
{a,c}
(iv)
{a,b}
(v)
{b,c,d}
Question
7
7.
Which of the following is a diagonal matrix ?
(i)
[
-4
0
-4
0
-6
0
-9
0
-9
]
(ii)
[
0
0
-4
0
-6
0
-9
0
0
]
(iii)
[
-4
0
0
0
-6
0
0
0
-9
]
(iv)
[
-4
0
-5
0
-6
0
0
0
-9
]
(v)
[
-4
0
0
0
-6
0
-5
0
-9
]
Question
8
8.
If A =
[
3
4
0
4
]
and B =
[
0
1
-4
3
]
, then
10
A
+
7
B =
(i)
[
27
47
-28
61
]
(ii)
[
30
50
-28
61
]
(iii)
[
30
47
-28
61
]
(iv)
[
30
47
-27
61
]
(v)
[
29
47
-28
61
]
Question
9
9.
Given A =
[
-1
-1
2
-2
4
-2
-4
-1
4
]
and B =
[
6
0
14
]
,
find P such that AP = B
(i)
[
0
2
5
]
(ii)
[
-3
2
4
]
(iii)
[
0
2
3
]
(iv)
[
2
2
4
]
(v)
[
0
2
4
]
Question
10
10.
If the order of matrix A is
m ✕ n
and B is
n ✕ o
and C is
o ✕ p
,
then the order of
(
A
✕
B
)
✕
C
is
(i)
m ✕ p
(ii)
m ✕ o
(iii)
o ✕ m
(iv)
p ✕ m
(v)
n ✕ p
Question
11
11.
Given A =
[
-2
8
7
-4
]
and B =
[
a
1
6
b
1
24
]
,
if BA = I find a and b
(i)
a =
1
8
, b =
1
22
(ii)
a =
1
22
, b =
7
48
(iii)
a =
1
12
, b =
7
48
(iv)
a =
1
12
, b =
1
8
Question
12
12.
The order of matrix A =
[
-2
2
4
]
is
(i)
2 ✕ 4
(ii)
2 ✕ 3
(iii)
1 ✕ 3
(iv)
1 ✕ 4
(v)
3 ✕ 1
Question
13
13.
Which of the following is a row matrix
(i)
[
8
9
1
4
]
(ii)
[
5
6
6
]
(iii)
[
1
2
]
(iv)
[
1
7
5
4
]
(v)
[
4
4
9
2
6
]
Question
14
14.
If A =
[
4
3
4
4
3
-3
-3
-3
-4
]
, then
5
A =
(i)
[
21
15
20
20
15
-15
-15
-15
-20
]
(ii)
[
20
14
20
20
15
-15
-15
-15
-20
]
(iii)
[
20
15
20
20
15
-15
-15
-15
-20
]
(iv)
[
20
15
20
20
12
-15
-15
-15
-20
]
(v)
[
20
18
20
20
15
-15
-15
-15
-20
]
Question
15
15.
If the order of matrix
(
A
✕
B
)
is
5 ✕ 2
and the order of B =
5 ✕ 2
,
then the order of A is ?
(i)
5 ✕ 4
(ii)
6 ✕ 6
(iii)
5 ✕ 5
(iv)
5 ✕ 6
(v)
6 ✕ 5
Question
16
16.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
3 ✕ 1 , 1 ✕ 3
(ii)
1 ✕ 2 , 2 ✕ 1
(iii)
1 ✕ 2 , 2 ✕ 3
(iv)
1 ✕ 3 , 2 ✕ 3
(v)
2 ✕ 3 , 3 ✕ 1
Question
17
17.
Given A =
[
3
-9
-5
8
]
find B such that AB = BA = A
(i)
[
1
0
0
0
]
(ii)
[
1
1
0
1
]
(iii)
[
1
0
-3
1
]
(iv)
[
1
0
0
4
]
(v)
[
1
0
0
1
]
Question
18
18.
If A =
[
4
7
-9
1
]
, then find B satisfying A
✕ B = A
(i)
[
1
-3
0
1
]
(ii)
[
1
0
0
1
]
(iii)
[
1
2
0
1
]
(iv)
[
1
0
0
0
]
(v)
[
2
0
0
1
]
Question
19
19.
Which of the following pairs of matrices can be multiplied?
(i)
[
8
-1
9
-3
]
,
[
4
6
0
-1
]
(ii)
[
8
-1
9
-3
]
,
[
-7
3
4
-9
4
6
]
(iii)
[
-9
3
3
]
,
[
-3
2
0
-9
-4
0
]
(iv)
[
8
-1
9
-3
]
,
[
-2
-1
]
(v)
[
9
9
-7
]
,
[
-7
3
4
-9
4
6
]
Question
20
20.
If A =
[
a
b
c
d
e
f
]
and B =
[
p
q
r
s
t
u
]
,
then
(
A
✕
B
)
=
(i)
[
p
a
+
q
d
p
b
+
q
e
p
c
+
q
f
r
a
+
s
d
r
b
+
s
e
r
c
+
s
f
t
a
+
u
d
t
b
+
u
e
t
c
+
u
f
]
(ii)
[
a
p
+
b
r
+
c
t
a
q
+
b
s
+
c
u
d
p
+
e
r
+
f
t
d
q
+
e
s
+
f
u
]
(iii)
[
a
p
+
b
r
+
c
t
d
p
+
e
r
+
f
t
a
q
+
b
s
+
c
u
d
q
+
e
s
+
f
u
]
(iv)
[
a
b
c
d
e
f
]
(v)
[
a
p
+
d
q
a
r
+
d
s
a
t
+
d
u
b
p
+
e
q
b
r
+
e
s
b
t
+
e
u
c
p
+
f
q
c
r
+
f
s
c
t
+
f
u
]
Question
21
21.
If A =
[
2
2
-4
2
-2
0
1
4
-4
]
and B =
[
-1
1
1
4
-2
-1
-3
4
-2
]
, then A
+
B =
(i)
[
1
3
-3
6
-4
-1
-2
8
-6
]
(ii)
[
1
3
-5
6
-4
-1
-2
8
-6
]
(iii)
[
1
3
-3
6
-4
0
-2
8
-6
]
(iv)
[
1
3
-4
6
-4
-1
-2
8
-6
]
(v)
[
1
3
-3
6
-4
-1
-2
10
-6
]
Question
22
22.
Which of the following matrices is a
3 ✕ 3
matrix ?
(i)
[
9
3
7
1
5
5
5
5
7
1
6
3
]
(ii)
[
4
7
1
7
4
1
1
9
7
]
(iii)
[
9
1
8
9
9
9
1
8
4
5
2
6
]
(iv)
[
1
9
5
9
9
9
7
4
2
9
6
9
9
3
9
7
]
(v)
[
1
4
6
8
4
4
3
2
4
9
1
3
8
8
8
2
]
Question
23
23.
If the order of matrix A is
m ✕ n
and B is
n ✕ o
,
then the order of
(
A
✕
B
)
is
(i)
m ✕ o
(ii)
o ✕ m
(iii)
m ✕ n
(iv)
n ✕ o
Question
24
24.
If A =
[
-1
-2
1
1
]
, B =
[
1
0
1
-2
]
and C =
[
0
2
-1
1
]
,
then A
✕
(B
+
C ) =
(i)
[
-1
-1
1
1
]
(ii)
[
-1
-3
1
1
]
(iii)
[
-1
0
4
1
]
(iv)
[
-1
0
1
1
]
(v)
[
0
0
1
1
]
Question
25
25.
If A =
[
-2
6
6
2
0
6
2
-3
1
]
and O =
[
0
0
0
0
0
0
0
0
0
]
, then A
+
O =
(i)
[
-2
6
6
2
0
6
2
-3
0
]
(ii)
[
-2
6
6
2
0
6
2
-2
1
]
(iii)
[
-2
6
6
2
0
6
-1
-3
1
]
(iv)
[
-2
6
6
2
0
6
2
-3
1
]
(v)
[
-2
6
6
2
0
6
2
-3
4
]
Assignment Key
1) (v)
2) (v)
3) (ii)
4) (iv)
5) (i)
6) (v)
7) (iii)
8) (iii)
9) (v)
10) (i)
11) (iii)
12) (iii)
13) (i)
14) (iii)
15) (iii)
16) (iv)
17) (v)
18) (ii)
19) (i)
20) (ii)
21) (i)
22) (ii)
23) (i)
24) (iv)
25) (iv)
