EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
If A =
[
a
b
c
d
e
f
]
and B =
[
p
q
r
s
t
u
]
,
then
(
A
✕
B
)
=
(i)
[
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
]
(ii)
[
a
b
c
d
e
f
]
(iii)
[
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
]
(iv)
[
a
p
+
b
r
+
c
t
d
p
+
e
r
+
f
t
a
q
+
b
s
+
c
u
d
q
+
e
s
+
f
u
]
(v)
[
a
p
+
b
r
+
c
t
a
q
+
b
s
+
c
u
d
p
+
e
r
+
f
t
d
q
+
e
s
+
f
u
]
Question
2
2.
If the order of matrix
(
A
✕
B
)
is
5 ✕ 4
and the order of B =
4 ✕ 4
,
then the order of A is ?
(i)
6 ✕ 4
(ii)
5 ✕ 3
(iii)
5 ✕ 5
(iv)
5 ✕ 4
(v)
6 ✕ 5
Question
3
3.
If A =
[
8
5
5
1
]
and B =
[
1
3
6
4
]
, find
(
A
−
B
)
2
(i)
[
47
8
-2
7
]
(ii)
[
47
8
-4
7
]
(iii)
[
47
8
-4
6
]
(iv)
[
44
8
-4
7
]
(v)
[
47
8
-4
8
]
Question
4
4.
If A =
[
2
-3
-2
0
4
-2
-4
3
0
]
, then
8
A =
(i)
[
16
-24
-16
0
32
-16
-32
24
0
]
(ii)
[
16
-24
-16
0
32
-16
-32
24
1
]
(iii)
[
19
-24
-16
0
32
-16
-32
24
0
]
(iv)
[
16
-27
-16
0
32
-16
-32
24
0
]
(v)
[
16
-24
-16
0
32
-16
-32
24
-1
]
Question
5
5.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
1 ✕ 2 , 2 ✕ 1
(ii)
3 ✕ 1 , 1 ✕ 3
(iii)
2 ✕ 3 , 3 ✕ 1
(iv)
3 ✕ 1 , 3 ✕ 2
(v)
1 ✕ 2 , 2 ✕ 3
Question
6
6.
Which of the following are true?
a)
A scalar matrix is an identity matrix
b)
An identity matrix is a square matrix
c)
A null matrix is a scalar matrix
d)
An identity matrix is a scalar matrix
(i)
{a,c,b}
(ii)
{c,d}
(iii)
{b,d}
(iv)
{a,b}
(v)
{a,d,b}
Question
7
7.
If A =
[
-8
-3
-5
6
]
and B =
[
4
-2
4
-2
]
, then A
+
B =
(i)
[
-4
-5
0
4
]
(ii)
[
-4
-5
-1
3
]
(iii)
[
-4
-5
-1
6
]
(iv)
[
-4
-5
-1
1
]
(v)
[
-4
-5
-1
4
]
Question
8
8.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
3 ✕ 2 , 1 ✕ 2
(ii)
1 ✕ 2 , 2 ✕ 1
(iii)
1 ✕ 2 , 2 ✕ 3
(iv)
2 ✕ 3 , 3 ✕ 1
(v)
3 ✕ 1 , 1 ✕ 3
Question
9
9.
If the order of matrix
(
A
✕
B
)
is
4 ✕ 3
and the order of A =
4 ✕ 3
,
then the order of B is ?
(i)
2 ✕ 3
(ii)
3 ✕ 3
(iii)
4 ✕ 3
(iv)
3 ✕ 4
(v)
4 ✕ 4
Question
10
10.
Which of the following are true ?
a)
If A X B is possible, the no of cols in A must be equal to no of cols in B
b)
If A X B is possible, the no of rows in A must be equal to no of cols in B
c)
If A X B is possible, the no of cols in A must be equal to no of rows in B
d)
If A X B is possible, the no of rows in A must be equal to no of rows in B
(i)
{d,a,c}
(ii)
{c}
(iii)
{b,c}
(iv)
{a,c}
Question
11
11.
If the elements of matrix A are multiplied with 0 , we get
(i)
multiplicative inverse of A
(ii)
additive inverse of A
(iii)
additive identity of A
(iv)
multiplicative identity of A
Question
12
12.
Which of the following are true ?
a)
Rectangular matrices can also have determinants
b)
A square matrix whose determinant is zero is called a non-singular matrix
c)
Only square matrices have determinants
d)
A square matrix whose determinant is zero is called a singular matrix
(i)
{a,c}
(ii)
{a,d,c}
(iii)
{c,d}
(iv)
{a,b,c}
(v)
{b,d}
Question
13
13.
Which of the following is a square matrix?
(i)
[
5
1
9
2
2
1
]
(ii)
[
4
9
]
(iii)
[
1
4
2
6
4
2
8
8
8
8
7
2
]
(iv)
[
1
6
9
6
6
9
]
(v)
[
3
5
2
6
]
Question
14
14.
If A =
[
1
-2
4
4
]
, B =
[
3
-9
-7
7
]
and C =
[
4
5
-1
5
]
,
then A
+
10
B
+
9
C =
(i)
[
67
-47
-78
119
]
(ii)
[
67
-47
-75
119
]
(iii)
[
67
-47
-76
119
]
(iv)
[
67
-44
-75
119
]
(v)
[
67
-47
-74
119
]
Question
15
15.
Which of the following pairs of matrices can be multiplied?
(i)
[
8
-6
-2
]
,
[
-9
-3
2
-1
-8
0
]
(ii)
[
3
2
2
]
,
[
-6
6
0
-7
-7
-6
]
(iii)
[
-4
-2
4
6
]
,
[
-5
6
]
(iv)
[
-5
6
]
,
[
-9
-3
2
-1
-8
0
]
(v)
[
-4
-2
4
6
]
,
[
-6
6
0
-7
-7
-6
]
Question
16
16.
If A =
[
2
3
-2
0
-2
-2
-1
1
1
]
and B =
[
2
1
2
2
-1
-2
1
1
-2
]
, then A
✕
B =
(i)
[
8
-3
2
-6
0
8
1
-1
-6
]
(ii)
[
8
-3
2
-6
0
8
1
0
-6
]
(iii)
[
8
-3
2
-6
-1
8
1
-1
-6
]
(iv)
[
10
-3
2
-6
0
8
1
-1
-6
]
(v)
[
8
-3
2
-6
0
5
1
-1
-6
]
Question
17
17.
The number of columns in matrix A =
[
2
3
8
4
]
is
(i)
0
(ii)
1
(iii)
2
(iv)
3
(v)
4
Question
18
18.
A
4 ✕ 3
matrix has
a)
7
rows and
3
columns
b)
4
rows and
12
columns
c)
4
rows and
3
columns
d)
3
rows and
4
columns
(i)
{b,c}
(ii)
{c}
(iii)
{d,a,c}
(iv)
{a,c}
Question
19
19.
Which of the following matrices is a
2 ✕ 2
matrix ?
(i)
[
3
5
8
3
6
3
6
3
9
]
(ii)
[
1
6
7
7
]
(iii)
[
5
4
5
6
8
2
]
(iv)
[
8
5
3
7
7
7
]
(v)
[
9
8
4
2
7
1
2
2
7
]
Question
20
20.
Which of the following pairs of matrices can be multiplied?
(i)
[
-6
-2
-3
]
,
[
4
8
-9
0
-2
-4
]
(ii)
[
6
8
-7
0
]
,
[
-4
4
1
1
]
(iii)
[
6
8
-7
0
]
,
[
6
-5
]
(iv)
[
6
8
-7
0
]
,
[
4
8
-9
0
-2
-4
]
(v)
[
-6
6
-4
]
,
[
2
8
7
-5
-5
1
]
Question
21
21.
Which of the following matrices is a
2 ✕ 3
matrix ?
(i)
[
4
6
6
1
3
2
4
6
3
5
5
2
]
(ii)
[
7
4
2
6
8
4
1
4
3
]
(iii)
[
3
4
2
2
3
9
]
(iv)
[
1
8
5
3
5
2
6
8
]
(v)
[
7
4
8
2
6
3
]
Question
22
22.
Find the
multiplicative
identity of matrix A =
[
2
2
-2
-4
2
-4
3
-4
-3
]
(i)
[
1
0
0
0
1
0
0
3
1
]
(ii)
[
1
0
0
0
1
0
0
0
1
]
(iii)
[
1
0
0
0
1
0
0
1
1
]
(iv)
[
1
0
0
0
1
0
0
0
0
]
(v)
[
1
0
0
0
1
-2
0
0
1
]
Question
23
23.
Which of the following matrices is a
2 ✕ 1
matrix ?
(i)
[
2
2
]
(ii)
[
6
5
]
(iii)
[
5
7
1
]
(iv)
[
3
3
6
1
3
7
]
(v)
[
5
4
5
5
]
Question
24
24.
Which of the following matrices is a
3 ✕ 2
matrix ?
(i)
[
2
9
6
6
8
1
8
3
5
]
(ii)
[
8
8
9
1
4
1
]
(iii)
[
2
1
4
5
1
5
]
(iv)
[
1
3
8
8
3
3
7
4
5
7
6
7
]
(v)
[
5
5
6
4
7
5
5
4
]
Question
25
25.
Express the following equation in the matrix form
a
1
x
+
b
1
y
+
c
1
= 0 and
a
2
x
+
b
2
y
+
c
2
= 0
(i)
[
a
1
b
1
a
2
b
2
]
[
c
1
c
2
]
+
[
x
y
]
= 0
(ii)
[
a
1
a
2
b
1
b
2
]
[
x
y
]
+
[
c
1
c
2
]
= 0
(iii)
[
a
1
b
1
a
2
b
2
]
[
x
y
]
+
[
c
1
c
2
]
= 0
(iv)
[
a
1
b
1
a
2
b
2
]
[
x
y
]
[
c
1
c
2
]
= 0
Assignment Key
1) (v)
2) (iv)
3) (ii)
4) (i)
5) (iv)
6) (iii)
7) (v)
8) (i)
9) (ii)
10) (ii)
11) (iii)
12) (iii)
13) (v)
14) (ii)
15) (iv)
16) (i)
17) (iii)
18) (ii)
19) (ii)
20) (ii)
21) (iii)
22) (ii)
23) (ii)
24) (iii)
25) (iii)
