EduSahara™ Assignment
Name : Matrix Concepts
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Find the transpose of matrix A =
[
3
3
7
6
]
(i)
[
3
7
4
6
]
(ii)
[
3
7
0
6
]
(iii)
[
3
9
3
6
]
(iv)
[
3
7
3
6
]
(v)
[
3
6
3
6
]
Question
2
2.
Which of the following is an identity matrix ?
(i)
[
1
0
-3
1
]
(ii)
[
1
0
1
1
]
(iii)
[
1
0
0
0
]
(iv)
[
1
0
0
3
]
(v)
[
1
0
0
1
]
Question
3
3.
The number of rows in matrix A =
[
6
4
4
5
4
5
4
5
5
]
is
(i)
4
(ii)
3
(iii)
2
(iv)
5
(v)
1
Question
4
4.
The number of columns in matrix A =
[
0
-8
7
2
]
is
(i)
4
(ii)
2
(iii)
3
(iv)
1
(v)
0
Question
5
5.
The order of matrix A =
[
0
0
5
]
is
(i)
3 ✕ 2
(ii)
4 ✕ 1
(iii)
3 ✕ 1
(iv)
2 ✕ 1
(v)
1 ✕ 3
Question
6
6.
Which of the following are true?
a)
An identity matrix is a square matrix
b)
A null matrix is a square matrix
c)
A column matrix is a square matrix
d)
A row matrix is a square matrix
(i)
{a}
(ii)
{d,b,a}
(iii)
{c,a}
(iv)
{b,a}
Question
7
7.
Which of the following are true?
a)
A scalar matrix has all elements with same value
b)
A unit matrix has only one row and one column
c)
A
1 ✕ 1
matrix has only one element
d)
A zero matrix is a square matrix
(i)
{b,c}
(ii)
{a,c,b}
(iii)
{a,b}
(iv)
{a,d,b}
(v)
{d,c}
Question
8
8.
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 a square matrix
c)
A rectangular matrix cannot be symmetric
d)
If a matrix is symmetric then it is equal to its transpose
(i)
{a,d}
(ii)
{a,b,c}
(iii)
{a,b}
(iv)
{b,c,d}
(v)
{a,c}
Question
9
9.
If the transpose of a matrix is equal to its additive inverse, that matrix is called ____?
(i)
scalar matrix
(ii)
skew symmetric matrix
(iii)
identity matrix
(iv)
symmetric matrix
Question
10
10.
Which of the following are true ?
a)
A square matrix whose determinant is zero is called a non-singular matrix
b)
Only square matrices have determinants
c)
A square matrix whose determinant is zero is called a singular matrix
d)
Rectangular matrices can also have determinants
(i)
{a,c,b}
(ii)
{a,d,b}
(iii)
{b,c}
(iv)
{a,b}
(v)
{d,c}
Question
11
11.
If the elements of matrix A are multiplied with -1 , we get
(i)
multiplicative identity of A
(ii)
additive identity of A
(iii)
additive inverse of A
(iv)
multiplicative inverse of A
Question
12
12.
If the elements of matrix A are multiplied with 0 , we get
(i)
additive identity of A
(ii)
additive inverse of A
(iii)
multiplicative identity of A
(iv)
multiplicative inverse of A
Question
13
13.
Which of the following are true?
a)
An identity matrix is a scalar matrix
b)
An identity matrix is a square matrix
c)
A null matrix is a scalar matrix
d)
A scalar matrix is an identity matrix
(i)
{a,b}
(ii)
{c,a}
(iii)
{d,b}
(iv)
{c,d,a}
(v)
{c,b,a}
Question
14
14.
A
3 ✕ 4
matrix has
a)
4
rows and
3
columns
b)
3
rows and
4
columns
c)
7
rows and
4
columns
d)
3
rows and
12
columns
(i)
{a,b}
(ii)
{c,b}
(iii)
{b}
(iv)
{d,a,b}
Question
15
15.
Which of the following are true for matrices A and B ?
a)
If A and B can be added, they must have the same order
b)
The orders of
(
A
✕
B
)
and
(
B
✕
A
)
are same
c)
If AB = 0, A = 0 or B = 0 or both A and B are zero matrices
d)
If A and B can be multiplied, they must have the same order
(i)
{c,a}
(ii)
{d,b,a}
(iii)
{b,a}
(iv)
{a}
Question
16
16.
If
(
A
+
B
)
= 0, then
a)
B is the additive identity of A
b)
A is the additive inverse of B
c)
A is the additive identity of B
d)
B is the additive inverse of A
(i)
{a,b}
(ii)
{c,d}
(iii)
{b,d}
(iv)
{a,d,b}
(v)
{a,c,b}
Question
17
17.
Which of the following is a square matrix?
(i)
[
2
2
5
4
2
1
5
6
2
7
7
3
]
(ii)
[
1
7
3
9
9
1
3
8
2
6
2
4
7
2
6
9
6
8
2
1
]
(iii)
[
2
8
5
2
2
4
4
3
2
]
(iv)
[
1
2
4
7
3
5
6
6
1
5
2
3
]
(v)
[
6
2
5
4
5
1
]
Question
18
18.
Which of the following is a rectangular matrix?
(i)
[
2
1
4
9
2
9
8
4
]
(ii)
[
4
8
8
5
5
5
7
5
5
9
6
3
3
3
4
1
]
(iii)
[
5
7
9
4
]
(iv)
[
4
5
3
4
4
2
6
5
3
]
(v)
[
8
]
Question
19
19.
Which of the following are true ?
a)
If matrices A & B can be multiplied, they must have the same order
b)
If AB = 0, then A = 0 or B = 0 or both A & B are 0
c)
If matrices A & B can be added, they must have the same order
d)
The order of
(
A
✕
B
)
and
(
B
✕
A
)
is same
(i)
{a,c}
(ii)
{d,a,c}
(iii)
{b,c}
(iv)
{c}
Question
20
20.
Which of the following are true for matrices A, B and C ?
a)
A
✕
(
B
✕
C
)
=
(
A
✕
B
)
✕
C
b)
(
A
✕
I
)
=
(
I
✕
A
)
= I
c)
A
✕
(
B
+
C
)
=
(
A
✕
B
)
+
(
A
✕
C
)
d)
(
A
✕
I
)
=
(
I
✕
A
)
= A
e)
(
A
+
B
)
✕
C
=
(
A
✕
B
)
+
(
A
✕
C
)
f)
(
A
✕
B
)
=
(
B
✕
A
)
(i)
{f,b,d}
(ii)
{e,a,c}
(iii)
{e,c}
(iv)
{b,a}
(v)
{a,c,d}
Question
21
21.
Which of the following is a row matrix
(i)
[
7
4
]
(ii)
[
7
3
7
]
(iii)
[
1
5
6
5
7
]
(iv)
[
2
6
3
9
]
(v)
[
5
9
]
Question
22
22.
Which of the following is a column matrix
(i)
[
1
3
8
1
2
8
3
7
1
]
(ii)
[
9
4
]
(iii)
[
4
3
4
5
]
(iv)
[
2
4
7
]
(v)
[
6
4
]
Question
23
23.
Which of the following is a diagonal matrix ?
(i)
[
2
0
2
0
-9
0
-8
0
-8
]
(ii)
[
2
0
-1
0
-9
0
0
0
-8
]
(iii)
[
2
0
0
0
-9
0
0
0
-8
]
(iv)
[
2
0
0
0
-9
0
-1
0
-8
]
(v)
[
0
0
2
0
-9
0
-8
0
0
]
Question
24
24.
The principal diagonal elements of the given matrix
[
-7
-1
-6
9
]
are
(i)
-7
,
9
(ii)
-7
,
-6
(iii)
-1
,
-6
(iv)
-1
,
9
Question
25
25.
The principal diagonal elements of the given matrix
[
5
1
-7
8
6
-5
-9
3
-1
]
are
(i)
5
,
-7
,
6
(ii)
-7
,
6
,
-9
(iii)
5
,
6
,
-1
(iv)
1
,
8
,
3
Question
26
26.
If A =
[
-1
8
1
-7
]
and the sum of the values of
elements of matrix kA =
6
, find k
(i)
7
(ii)
4
(iii)
6
(iv)
5
(v)
9
Assignment Key
1) (iv)
2) (v)
3) (ii)
4) (ii)
5) (iii)
6) (i)
7) (i)
8) (iv)
9) (ii)
10) (iii)
11) (iii)
12) (i)
13) (i)
14) (iii)
15) (iv)
16) (iii)
17) (iii)
18) (i)
19) (iv)
20) (v)
21) (i)
22) (v)
23) (iii)
24) (i)
25) (iii)
26) (iii)
