EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following are true?
a)
A
1 ✕ 1
matrix has only one element
b)
A zero matrix is a square matrix
c)
A unit matrix has only one row and one column
d)
A scalar matrix has all elements with same value
(i)
{b,a}
(ii)
{a,c}
(iii)
{b,c,a}
(iv)
{d,c}
(v)
{b,d,a}
Question
2
2.
The order of matrix A =
[
-5
-1
1
]
is
(i)
1 ✕ 3
(ii)
2 ✕ 4
(iii)
1 ✕ 4
(iv)
2 ✕ 3
(v)
3 ✕ 1
Question
3
3.
If a matrix has
16
elements, what are the possible orders it can have?
(i)
{2 ✕ 8,4 ✕ 4,8 ✕ 2,16 ✕ 1}
(ii)
{1 ✕ 16,4 ✕ 4,8 ✕ 2,16 ✕ 1}
(iii)
{1 ✕ 16,2 ✕ 8,4 ✕ 4,8 ✕ 2,16 ✕ 1}
(iv)
{1 ✕ 16,2 ✕ 8,8 ✕ 2,16 ✕ 1}
Question
4
4.
The order of matrix A =
[
5
-2
]
is
(i)
2 ✕ 2
(ii)
2 ✕ 3
(iii)
2 ✕ 1
(iv)
1 ✕ 2
(v)
1 ✕ 3
Question
5
5.
If A =
[
1
4
-1
-3
]
and B =
[
4
3
-4
-3
]
, then
4
A
+
9
B =
(i)
[
40
43
-40
-40
]
(ii)
[
40
43
-40
-39
]
(iii)
[
40
43
-40
-37
]
(iv)
[
40
41
-40
-39
]
(v)
[
40
44
-40
-39
]
Question
6
6.
If A =
[
a
b
c
d
]
and B =
[
p
q
r
s
]
,
then
(
A
✕
B
)
=
(i)
[
a
p
+
c
q
a
r
+
c
s
b
p
+
d
q
b
r
+
d
s
]
(ii)
[
a
p
+
b
r
a
q
+
b
s
c
p
+
d
r
c
q
+
d
s
]
(iii)
[
a
p
+
b
q
a
r
+
b
s
c
p
+
d
q
c
r
+
d
s
]
(iv)
[
p
a
+
q
c
p
b
+
q
d
r
a
+
s
c
r
b
+
s
d
]
(v)
[
a
p
+
b
r
c
p
+
d
r
a
q
+
b
s
c
q
+
d
s
]
Question
7
7.
If A =
[
7
6
4
3
]
and B =
[
9
9
2
1
]
, find
A
2
+
B
2
−
2AB
(i)
[
22
12
-24
-26
]
(ii)
[
24
12
-24
-26
]
(iii)
[
22
13
-24
-26
]
(iv)
[
22
12
-24
-28
]
(v)
[
22
12
-24
-27
]
Question
8
8.
If A =
[
-6
-4
-2
-9
]
, then find B satisfying A
✕ B = A
(i)
[
1
0
0
1
]
(ii)
[
1
-1
0
1
]
(iii)
[
1
0
1
1
]
(iv)
[
1
2
0
1
]
(v)
[
1
-3
0
1
]
Question
9
9.
The order of matrix A =
[
-4
-5
]
is
(i)
1 ✕ 1
(ii)
3 ✕ 1
(iii)
2 ✕ 1
(iv)
1 ✕ 2
(v)
2 ✕ 2
Question
10
10.
Which of the following matrices can be added to
[
9
5
9
5
]
?
(i)
[
7
8
5
6
7
6
8
3
3
9
6
9
]
(ii)
[
4
3
8
1
3
9
]
(iii)
[
1
9
9
8
2
6
]
(iv)
[
4
1
9
1
]
(v)
[
7
3
]
Question
11
11.
If A =
[
5
5
3
-3
]
and B =
[
-1
4
-4
6
]
, then
4
A
−
6
B =
(i)
[
26
-4
36
-49
]
(ii)
[
28
-4
36
-48
]
(iii)
[
26
-4
36
-48
]
(iv)
[
23
-4
36
-48
]
(v)
[
26
-4
36
-47
]
Question
12
12.
Which of the following are true?
a)
If a matrix is symmetric, then it is a square matrix
b)
A matrix is symmetric if the principal diagonal elements are same
c)
If a matrix is symmetric then it is equal to its transpose
d)
A rectangular matrix cannot be symmetric
(i)
{b,a}
(ii)
{b,c}
(iii)
{b,a,c}
(iv)
{b,d}
(v)
{a,c,d}
Question
13
13.
Matrix A =
[
-4
4
-2
-2
1
-1
1
-4
-2
]
is the additive inverse of
(i)
[
4
-4
2
2
-1
1
-1
4
2
]
(ii)
[
4
-4
2
2
0
1
-1
4
2
]
(iii)
[
4
-4
2
2
-1
1
-1
4
0
]
(iv)
[
6
-4
2
2
-1
1
-1
4
2
]
(v)
[
4
-5
2
2
-1
1
-1
4
2
]
Question
14
14.
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)
2 ✕ 3 , 3 ✕ 1
(iii)
1 ✕ 2 , 2 ✕ 3
(iv)
1 ✕ 2 , 2 ✕ 1
(v)
1 ✕ 3 , 2 ✕ 3
Question
15
15.
If A =
[
7
-8
3
-3
]
, B =
[
7
9
-2
-8
]
and C =
[
-6
1
9
7
]
,
then
9
A
−
8
B
+
8
C
=
(i)
[
-41
-133
115
93
]
(ii)
[
-41
-136
115
94
]
(iii)
[
-41
-136
115
93
]
(iv)
[
-41
-136
115
92
]
(v)
[
-41
-136
112
93
]
Question
16
16.
Which of the following are true ?
a)
If A X B is possible, the no of rows in A must be equal to no of cols in B
b)
If A X B is possible, the no of cols 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)
{a,c}
(ii)
{c}
(iii)
{b,c}
(iv)
{d,a,c}
Question
17
17.
If A and B are given as below, neither
(
A
✕
B
)
nor
(
B
✕
A
)
is possible for which of the following pairs?
(i)
2 ✕ 3 , 3 ✕ 1
(ii)
3 ✕ 1 , 1 ✕ 3
(iii)
3 ✕ 1 , 3 ✕ 2
(iv)
1 ✕ 2 , 2 ✕ 1
(v)
1 ✕ 2 , 2 ✕ 3
Question
18
18.
If the transpose of a matrix is equal to its additive inverse, that matrix is called ____?
(i)
scalar matrix
(ii)
identity matrix
(iii)
symmetric matrix
(iv)
skew symmetric matrix
Question
19
19.
The number of rows in matrix A =
[
6
5
6
6
5
4
4
4
5
]
is
(i)
4
(ii)
3
(iii)
1
(iv)
5
(v)
2
Question
20
20.
Find the
multiplicative
identity of matrix A =
[
-3
-3
8
-1
]
(i)
[
1
0
-3
1
]
(ii)
[
1
0
2
1
]
(iii)
[
2
0
0
1
]
(iv)
[
1
0
0
0
]
(v)
[
1
0
0
1
]
Question
21
21.
The principal diagonal elements of the given matrix
[
9
-6
-5
-3
]
are
(i)
9
,
-5
(ii)
-6
,
-3
(iii)
-6
,
-5
(iv)
9
,
-3
Question
22
22.
If A =
[
(
−
7
)
7
]
, B =
[
x
y
]
, then
(
A
✕
B
)
=
(i)
[
(
−
7
x
)
(
−
7
y
)
7
x
7
y
]
(ii)
[
(
−
7
x
)
7
x
(
−
7
y
)
7
y
]
(iii)
[
(
−
7
x
+
7
y
)
(
−
7
x
+
7
y
)
]
(iv)
[
(
−
7
x
+
7
y
)
(
−
7
x
+
7
y
)
]
(v)
[
(
−
7
x
+
7
y
)
]
Question
23
23.
If A =
[
7
1
2
7
]
and B =
[
4
5
7
6
]
, find
A
2
+
B
2
+
2AB
(i)
[
172
146
212
225
]
(ii)
[
172
148
212
226
]
(iii)
[
172
146
213
226
]
(iv)
[
172
146
212
226
]
(v)
[
172
143
212
226
]
Question
24
24.
The order of matrix A =
[
0
1
-1
-1
-3
-2
3
0
2
]
is
(i)
3 ✕ 3
(ii)
2 ✕ 3
(iii)
4 ✕ 3
(iv)
3 ✕ 4
(v)
3 ✕ 2
Question
25
25.
If A =
[
1
-2
-2
2
]
, B =
[
1
-1
1
2
]
and C =
[
-1
0
2
2
]
,
then (A
✕
B)
+
C =
(i)
[
-3
-5
2
8
]
(ii)
[
-5
-5
2
8
]
(iii)
[
-2
-5
2
8
]
(iv)
[
-2
-5
4
8
]
(v)
[
-2
-4
2
8
]
Assignment Key
1) (ii)
2) (i)
3) (iii)
4) (iv)
5) (ii)
6) (ii)
7) (i)
8) (i)
9) (iii)
10) (iv)
11) (iii)
12) (v)
13) (i)
14) (v)
15) (iii)
16) (ii)
17) (iii)
18) (iv)
19) (ii)
20) (v)
21) (iv)
22) (v)
23) (iv)
24) (i)
25) (iii)
