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
g
h
i
]
and B =
[
p
q
r
s
t
u
v
w
x
]
,
then
(
A
✕
B
)
=
(i)
[
a
p
+
b
s
+
c
v
d
p
+
e
s
+
f
v
g
p
+
h
s
+
i
v
a
q
+
b
t
+
c
w
d
q
+
e
t
+
f
w
g
q
+
h
t
+
i
w
a
r
+
b
u
+
c
x
d
r
+
e
u
+
f
x
g
r
+
h
u
+
i
x
]
(ii)
[
a
p
+
b
q
+
c
r
a
s
+
b
t
+
c
u
a
v
+
b
w
+
c
x
d
p
+
e
q
+
f
r
d
s
+
e
t
+
f
u
d
v
+
e
w
+
f
x
g
p
+
h
q
+
i
r
g
s
+
h
t
+
i
u
g
v
+
h
w
+
i
x
]
(iii)
[
p
a
+
q
d
+
r
g
p
b
+
q
e
+
r
h
p
c
+
q
f
+
r
i
s
a
+
t
d
+
u
g
s
b
+
t
e
+
u
h
s
c
+
t
f
+
u
i
v
a
+
w
d
+
x
g
v
b
+
w
e
+
x
h
v
c
+
w
f
+
x
i
]
(iv)
[
a
p
+
b
s
+
c
v
a
q
+
b
t
+
c
w
a
r
+
b
u
+
c
x
d
p
+
e
s
+
f
v
d
q
+
e
t
+
f
w
d
r
+
e
u
+
f
x
g
p
+
h
s
+
i
v
g
q
+
h
t
+
i
w
g
r
+
h
u
+
i
x
]
(v)
[
a
p
+
d
q
+
g
r
a
s
+
d
t
+
g
u
a
v
+
d
w
+
g
x
b
p
+
e
q
+
h
r
b
s
+
e
t
+
h
u
b
v
+
e
w
+
h
x
c
p
+
f
q
+
i
r
c
s
+
f
t
+
i
u
c
v
+
f
w
+
i
x
]
Question
2
2.
If A =
[
a
11
a
12
a
21
a
22
]
and B =
[
b
11
b
12
b
21
b
22
]
,
then
(
A
✕
B
)
=
(i)
[
a
11
b
11
+
a
12
b
12
a
11
b
21
+
a
12
b
22
a
21
b
11
+
a
22
b
12
a
21
b
21
+
a
22
b
22
]
(ii)
[
b
11
a
11
+
b
12
a
21
b
11
a
12
+
b
12
a
22
b
21
a
11
+
b
22
a
21
b
21
a
12
+
b
22
a
22
]
(iii)
[
a
11
b
11
+
a
21
b
12
a
11
b
21
+
a
21
b
22
a
12
b
11
+
a
22
b
12
a
12
b
21
+
a
22
b
22
]
(iv)
[
a
11
b
11
+
a
12
b
21
a
11
b
12
+
a
12
b
22
a
21
b
11
+
a
22
b
21
a
21
b
12
+
a
22
b
22
]
(v)
[
a
11
b
11
+
a
12
b
21
a
21
b
11
+
a
22
b
21
a
11
b
12
+
a
12
b
22
a
21
b
12
+
a
22
b
22
]
Question
3
3.
The principal diagonal elements of the given matrix
[
1
-2
7
-4
-8
8
9
-5
-9
]
are
(i)
1
,
7
,
-8
(ii)
7
,
-8
,
9
(iii)
-2
,
-4
,
-5
(iv)
1
,
-8
,
-9
Question
4
4.
Which of the following are true?
a)
A rectangular matrix cannot be symmetric
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 matrix is symmetric if the principal diagonal elements are same
(i)
{d,a,b}
(ii)
{d,a}
(iii)
{d,c}
(iv)
{a,b,c}
(v)
{d,b}
Question
5
5.
The order of matrix A =
[
-3
-1
-4
4
3
0
]
is
(i)
2 ✕ 3
(ii)
4 ✕ 2
(iii)
3 ✕ 3
(iv)
3 ✕ 2
(v)
2 ✕ 2
Question
6
6.
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 scalar matrix has all elements with same value
d)
A unit matrix has only one row and one column
(i)
{c,d}
(ii)
{b,a}
(iii)
{a,d}
(iv)
{b,d,a}
(v)
{b,c,a}
Question
7
7.
If A =
[
0
0
0
0
1
1
2
3
-2
]
and B =
[
3
3
-2
-2
3
3
3
1
3
]
, then A
✕
B =
(i)
[
0
0
0
1
4
6
-7
13
-1
]
(ii)
[
0
0
0
1
4
6
-6
13
-1
]
(iii)
[
0
0
0
1
4
6
-5
13
-1
]
(iv)
[
0
0
2
1
4
6
-6
13
-1
]
(v)
[
0
0
-3
1
4
6
-6
13
-1
]
Question
8
8.
If A =
[
9
2
6
1
]
and B =
[
9
2
7
3
]
, find
A
2
−
B
2
(i)
[
-2
-4
-22
-10
]
(ii)
[
-2
-4
-25
-10
]
(iii)
[
-2
-4
-24
-10
]
(iv)
[
-2
-4
-23
-10
]
(v)
[
-2
-6
-24
-10
]
Question
9
9.
Which of the following are true for matrices A, B and C ?
a)
(
A
✕
I
)
=
(
I
✕
A
)
= A
b)
(
A
✕
I
)
=
(
I
✕
A
)
= I
c)
A
✕
(
B
✕
C
)
=
(
A
✕
B
)
✕
C
d)
(
A
✕
B
)
=
(
B
✕
A
)
e)
A
✕
(
B
+
C
)
=
(
A
✕
B
)
+
(
A
✕
C
)
f)
(
A
+
B
)
✕
C
=
(
A
✕
B
)
+
(
A
✕
C
)
(i)
{f,b,e}
(ii)
{d,a,c}
(iii)
{a,c,e}
(iv)
{d,c}
(v)
{b,a}
Question
10
10.
Which of the following is a rectangular matrix?
(i)
[
3
6
7
3
5
6
]
(ii)
[
2
]
(iii)
[
1
9
6
8
3
9
4
1
9
5
5
7
5
8
2
7
]
(iv)
[
8
6
4
4
5
5
6
8
7
]
(v)
[
7
3
5
8
]
Question
11
11.
If A =
[
-7
-6
5
5
]
, B =
[
1
-5
9
0
]
and C =
[
3
0
7
-7
]
,
then A
+
7
B
+
4
C =
(i)
[
13
-41
96
-23
]
(ii)
[
12
-41
96
-20
]
(iii)
[
12
-41
96
-26
]
(iv)
[
12
-41
96
-24
]
(v)
[
12
-41
96
-23
]
Question
12
12.
Which of the following matrices is a
3 ✕ 2
matrix ?
(i)
[
2
9
9
2
3
9
]
(ii)
[
9
2
4
9
1
9
6
6
]
(iii)
[
2
3
9
7
5
5
2
3
8
]
(iv)
[
3
4
9
1
6
6
9
6
4
6
8
3
]
(v)
[
8
6
4
9
6
4
]
Question
13
13.
If A =
[
-3
-2
-2
0
-3
-2
-3
2
2
]
, then
A
2
=
(i)
[
15
8
6
6
5
2
3
4
4
]
(ii)
[
15
8
6
6
8
2
3
4
6
]
(iii)
[
15
8
6
6
5
2
3
4
6
]
(iv)
[
15
9
6
6
5
2
3
4
6
]
(v)
[
15
8
6
5
5
2
3
4
6
]
Question
14
14.
Which of the following are true ?
a)
If matrices A & B can be multiplied, they must have the same order
b)
If matrices A & B can be added, they must have the same order
c)
If AB = 0, then A = 0 or B = 0 or both A & B are 0
d)
The order of
(
A
✕
B
)
and
(
B
✕
A
)
is same
(i)
{d,a,b}
(ii)
{a,b}
(iii)
{c,b}
(iv)
{b}
Question
15
15.
If A =
[
4
3
6
3
]
and B =
[
6
3
2
6
]
, find
(
A
+
B
)
(
A
−
B
)
(i)
[
4
-18
20
-29
]
(ii)
[
4
-19
20
-27
]
(iii)
[
4
-18
20
-26
]
(iv)
[
4
-18
20
-24
]
(v)
[
4
-18
20
-27
]
Question
16
16.
If X + Y =
[
4
7
-5
-7
]
&
X - Y =
[
-10
-1
13
-5
]
, find X and Y
(i)
[
-3
3
4
-6
]
,
[
7
7
-9
-1
]
(ii)
[
-3
3
4
-6
]
,
[
7
4
-9
-1
]
(iii)
[
7
4
-9
-1
]
,
[
-3
3
4
-6
]
(iv)
[
-4
3
4
-6
]
,
[
7
4
-9
-1
]
Question
17
17.
Which of the following pairs of matrices can be multiplied?
(i)
[
-3
-1
4
]
,
[
4
6
-7
-2
7
7
]
(ii)
[
-7
-7
0
-3
]
,
[
-4
-9
]
(iii)
[
-7
-3
6
]
,
[
0
6
-9
-2
-3
-8
]
(iv)
[
-7
-7
0
-3
]
,
[
-3
8
-4
9
]
(v)
[
-7
-7
0
-3
]
,
[
0
6
-9
-2
-3
-8
]
Question
18
18.
If A =
[
a
b
c
d
]
and B =
[
2
4
5
9
]
and if A = B,
find the values of a, b, c and d
(i)
a = 2, b = 9, c = 4, d = 5
(ii)
a = 2, b = 4, c = 5, d = 9
(iii)
a = 9, b = 5, c = 4, d = 2
Question
19
19.
If A =
[
2
-2
1
0
]
, then find B satisfying A
+
B = I
(i)
[
-1
2
-1
1
]
(ii)
[
-1
1
-1
1
]
(iii)
[
-3
2
-1
1
]
(iv)
[
-1
2
-1
2
]
(v)
[
-1
2
-1
4
]
Question
20
20.
If A =
[
-8
5
-5
6
]
and B =
[
0
-3
5
5
]
, then A
−
B =
(i)
[
-10
8
-10
1
]
(ii)
[
-8
8
-10
3
]
(iii)
[
-7
8
-10
1
]
(iv)
[
-8
8
-10
1
]
(v)
[
-9
8
-10
1
]
Question
21
21.
If B =
[
3
3
9
2
]
and C =
[
42
14
]
and
(
A
✕
B
)
= C , find A
(i)
[
2
4
]
(ii)
[
5
4
]
(iii)
[
2
3
]
(iv)
[
2
2
]
(v)
[
2
5
]
Question
22
22.
If A =
[
a
b
c
d
]
and B =
[
p
q
r
s
]
,
then
(
A
✕
B
)
=
(i)
[
a
p
+
b
r
c
p
+
d
r
a
q
+
b
s
c
q
+
d
s
]
(ii)
[
a
p
+
c
q
a
r
+
c
s
b
p
+
d
q
b
r
+
d
s
]
(iii)
[
p
a
+
q
c
p
b
+
q
d
r
a
+
s
c
r
b
+
s
d
]
(iv)
[
a
p
+
b
q
a
r
+
b
s
c
p
+
d
q
c
r
+
d
s
]
(v)
[
a
p
+
b
r
a
q
+
b
s
c
p
+
d
r
c
q
+
d
s
]
Question
23
23.
If A =
[
0
1
0
2
]
, B =
[
-2
0
2
-1
]
and C =
[
0
-1
0
-1
]
,
then (A
+
B)
+
C =
(i)
[
-2
-1
2
0
]
(ii)
[
-2
0
2
1
]
(iii)
[
-2
0
2
0
]
(iv)
[
-2
0
5
0
]
(v)
[
-2
-3
2
0
]
Question
24
24.
The order of matrix A =
[
-3
-2
5
]
is
(i)
1 ✕ 3
(ii)
3 ✕ 1
(iii)
2 ✕ 3
(iv)
1 ✕ 4
(v)
2 ✕ 4
Question
25
25.
Which of the following matrices is comparable to the
given matrix
[
6
5
1
5
]
?
(i)
[
9
8
]
(ii)
[
8
6
2
4
2
1
]
(iii)
[
9
4
1
5
8
2
]
(iv)
[
4
1
3
3
5
4
3
2
2
5
9
3
]
(v)
[
4
5
9
2
]
Assignment Key
1) (iv)
2) (iv)
3) (iv)
4) (iv)
5) (iv)
6) (iii)
7) (ii)
8) (iii)
9) (iii)
10) (i)
11) (v)
12) (v)
13) (iii)
14) (iv)
15) (v)
16) (ii)
17) (iv)
18) (ii)
19) (i)
20) (iv)
21) (i)
22) (v)
23) (iii)
24) (i)
25) (v)
