EduSahara™ Assignment
Name : Matrix Miscellaneous
Chapter : Matrices
Grade : ICSE Grade X
License : Non Commercial Use
Question
1
1.
Which of the following is an identity matrix ?
(i)
[
4
0
0
1
]
(ii)
[
1
0
-1
1
]
(iii)
[
1
0
0
1
]
(iv)
[
1
-3
0
1
]
(v)
[
1
1
0
1
]
Question
2
2.
Matrix A =
[
-1
2
3
0
0
1
-4
0
0
]
is the additive inverse of
(i)
[
1
-5
-3
0
0
-1
4
0
0
]
(ii)
[
1
-2
-2
0
0
-1
4
0
0
]
(iii)
[
1
-2
-3
0
0
-1
4
0
0
]
(iv)
[
1
-2
-3
0
2
-1
4
0
0
]
(v)
[
1
-2
-4
0
0
-1
4
0
0
]
Question
3
3.
If A =
[
-4
-1
3
0
-4
-3
1
2
-4
]
, then
5
A =
(i)
[
-20
-5
15
0
-20
-15
5
10
-21
]
(ii)
[
-20
-5
15
0
-20
-15
5
10
-20
]
(iii)
[
-20
-5
15
0
-20
-15
5
10
-22
]
(iv)
[
-20
-5
15
2
-20
-15
5
10
-20
]
(v)
[
-20
-5
15
0
-20
-15
6
10
-20
]
Question
4
4.
If A =
[
-1
-1
2
-2
3
-5
2
-4
1
]
and O =
[
0
0
0
0
0
0
0
0
0
]
, then A
+
O =
(i)
[
-1
-1
2
-2
3
-5
2
-4
1
]
(ii)
[
-1
-1
2
-2
3
-4
2
-4
1
]
(iii)
[
-1
-1
2
-2
3
-5
1
-4
1
]
(iv)
[
-1
-1
2
-2
3
-5
2
-1
1
]
(v)
[
-1
-1
2
-2
1
-5
2
-4
1
]
Question
5
5.
If A =
[
-8
6
5
1
]
, then find B satisfying A
+ B = O
(i)
[
8
-6
-5
2
]
(ii)
[
8
-6
-5
-1
]
(iii)
[
8
-6
-5
-2
]
(iv)
[
8
-9
-5
-1
]
(v)
[
8
-5
-5
-1
]
Question
6
6.
If A =
[
4
-2
3
3
]
, then find B satisfying A
+
B = I
(i)
[
-3
2
-3
1
]
(ii)
[
-3
2
-4
-2
]
(iii)
[
-3
2
-3
-2
]
(iv)
[
-3
2
-3
-1
]
(v)
[
-6
2
-3
-2
]
Question
7
7.
If A =
[
4
3
3
-1
]
, then find AI
(i)
[
4
3
2
-1
]
(ii)
[
4
3
3
-1
]
(iii)
[
1
3
3
-1
]
(iv)
[
4
6
3
-1
]
(v)
[
4
4
3
-1
]
Question
8
8.
If A =
[
-5
5
-6
3
]
, then find B satisfying A
+ B = A
(i)
[
0
0
0
-2
]
(ii)
[
0
0
0
-1
]
(iii)
[
0
1
0
0
]
(iv)
[
0
0
0
0
]
(v)
[
0
0
0
3
]
Question
9
9.
If A =
[
8
-3
3
4
]
, then find B satisfying A
✕ B = A
(i)
[
1
0
0
1
]
(ii)
[
1
0
1
1
]
(iii)
[
1
-1
0
1
]
(iv)
[
1
2
0
1
]
(v)
[
1
-2
0
1
]
Question
10
10.
Which of the following are true?
a)
A row matrix is a square matrix
b)
A null matrix is a square matrix
c)
A column matrix is a square matrix
d)
An identity matrix is a square matrix
(i)
{b,d}
(ii)
{a,d}
(iii)
{d}
(iv)
{c,a,d}
Question
11
11.
Which of the following are true?
a)
A scalar matrix has all elements with same value
b)
A
1 ✕ 1
matrix has only one element
c)
A unit matrix has only one row and one column
d)
A zero matrix is a square matrix
(i)
{a,c,b}
(ii)
{b,c}
(iii)
{a,b}
(iv)
{a,d,b}
(v)
{d,c}
Question
12
12.
Which of the following are true?
a)
A rectangular matrix cannot be symmetric
b)
If a matrix is symmetric, then it is a square matrix
c)
If a matrix is symmetric then it is equal to its transpose
d)
A matrix is symmetric if the principal diagonal elements are same
(i)
{a,b,c}
(ii)
{d,a,b}
(iii)
{d,a}
(iv)
{d,c}
(v)
{d,b}
Question
13
13.
If the transpose of a matrix is equal to its additive inverse, that matrix is called ____?
(i)
skew symmetric matrix
(ii)
identity matrix
(iii)
symmetric matrix
(iv)
scalar matrix
Question
14
14.
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)
{d,c}
(ii)
{b,c}
(iii)
{a,b}
(iv)
{a,c,b}
(v)
{a,d,b}
Question
15
15.
If the elements of matrix A are multiplied with -1 , we get
(i)
multiplicative inverse of A
(ii)
additive inverse of A
(iii)
multiplicative identity of A
(iv)
additive identity of A
Question
16
16.
If the elements of matrix A are multiplied with 0 , we get
(i)
multiplicative identity of A
(ii)
multiplicative inverse of A
(iii)
additive identity of A
(iv)
additive inverse of A
Question
17
17.
Which of the following are true?
a)
An identity matrix is a square matrix
b)
A null matrix is a scalar matrix
c)
A scalar matrix is an identity matrix
d)
An identity matrix is a scalar matrix
(i)
{b,d,a}
(ii)
{c,d}
(iii)
{a,d}
(iv)
{b,c,a}
(v)
{b,a}
Question
18
18.
A
3 ✕ 2
matrix has
a)
2
rows and
3
columns
b)
3
rows and
6
columns
c)
5
rows and
2
columns
d)
3
rows and
2
columns
(i)
{d}
(ii)
{a,d}
(iii)
{c,a,d}
(iv)
{b,d}
Question
19
19.
Which of the following are true for matrices A and B ?
a)
If AB = 0, A = 0 or B = 0 or both A and B are zero matrices
b)
The orders of
(
A
✕
B
)
and
(
B
✕
A
)
are same
c)
If A and B can be added, they must have the same order
d)
If A and B can be multiplied, they must have the same order
(i)
{b,c}
(ii)
{c}
(iii)
{a,c}
(iv)
{d,a,c}
Question
20
20.
If
(
A
+
B
)
= 0, then
a)
B is the additive identity of A
b)
A is the additive identity of B
c)
A is the additive inverse of B
d)
B is the additive inverse of A
(i)
{b,d}
(ii)
{c,d}
(iii)
{a,d,c}
(iv)
{a,b,c}
(v)
{a,c}
Question
21
21.
Which of the following is a square matrix?
(i)
[
9
8
2
2
6
9
8
6
4
2
4
8
]
(ii)
[
1
9
1
7
9
4
]
(iii)
[
5
5
4
1
]
(iv)
[
3
4
]
(v)
[
7
2
3
5
1
5
]
Question
22
22.
Which of the following is a rectangular matrix?
(i)
[
6
2
6
7
2
1
]
(ii)
[
5
7
4
9
]
(iii)
[
4
9
8
5
5
7
1
8
8
]
(iv)
[
1
]
(v)
[
9
3
7
1
2
7
7
8
8
9
9
6
3
8
9
8
]
Question
23
23.
Which of the following are true ?
a)
If matrices A & B can be added, they must have the same order
b)
If matrices A & B can be multiplied, 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)
{b,a}
(ii)
{a}
(iii)
{d,b,a}
(iv)
{c,a}
Question
24
24.
Which of the following are true for matrices A, B and C ?
a)
A
✕
(
B
+
C
)
=
(
A
✕
B
)
+
(
A
✕
C
)
b)
(
A
✕
B
)
=
(
B
✕
A
)
c)
(
A
+
B
)
✕
C
=
(
A
✕
B
)
+
(
A
✕
C
)
d)
(
A
✕
I
)
=
(
I
✕
A
)
= I
e)
A
✕
(
B
✕
C
)
=
(
A
✕
B
)
✕
C
f)
(
A
✕
I
)
=
(
I
✕
A
)
= A
(i)
{c,e}
(ii)
{c,a,e}
(iii)
{b,a}
(iv)
{d,b,f}
(v)
{a,e,f}
Question
25
25.
If the order of matrix A is
m ✕ n
and B is
n ✕ o
,
then the order of
(
A
✕
B
)
is
(i)
m ✕ n
(ii)
o ✕ m
(iii)
n ✕ o
(iv)
m ✕ o
Question
26
26.
Which of the following is a row matrix
(i)
[
9
5
1
]
(ii)
[
7
3
5
2
6
]
(iii)
[
1
1
]
(iv)
[
8
9
6
6
]
(v)
[
5
2
7
]
Question
27
27.
Which of the following is a column matrix
(i)
[
4
7
9
8
1
2
7
4
3
]
(ii)
[
7
2
6
]
(iii)
[
7
4
4
3
]
(iv)
[
2
1
6
1
]
(v)
[
3
7
]
Question
28
28.
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 rows in A must be equal to no of rows 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 cols in A must be equal to no of cols in B
(i)
{d,a,c}
(ii)
{a,c}
(iii)
{b,c}
(iv)
{c}
Question
29
29.
Which of the following is a diagonal matrix ?
(i)
[
4
0
4
0
-9
0
-9
0
-9
]
(ii)
[
4
0
0
0
-9
0
0
0
-9
]
(iii)
[
0
0
4
0
-9
0
-9
0
0
]
(iv)
[
4
0
3
0
-9
0
0
0
-9
]
(v)
[
4
0
0
0
-9
0
3
0
-9
]
Question
30
30.
If A =
[
3
0
0
x
]
is a scalar matrix, then x = ?
(i)
0
(ii)
9
(iii)
3
(iv)
1
(v)
x
Question
31
31.
The principal diagonal elements of the given matrix
[
-4
-7
-1
1
]
are
(i)
-7
,
-1
(ii)
-4
,
1
(iii)
-4
,
-1
(iv)
-7
,
1
Question
32
32.
The principal diagonal elements of the given matrix
[
4
9
-4
-1
1
6
2
-2
8
]
are
(i)
9
,
-1
,
-2
(ii)
4
,
1
,
8
(iii)
-4
,
1
,
2
(iv)
4
,
-4
,
1
Question
33
33.
If A =
[
3
9
6
1
]
and the sum of the values of
elements of matrix kA =
171
, find k
(i)
7
(ii)
12
(iii)
10
(iv)
9
(v)
8
Question
34
34.
If A =
[
-4
-3
-9
0
]
, the value of -A =
(i)
[
7
3
9
0
]
(ii)
[
4
3
9
0
]
(iii)
[
4
3
8
0
]
(iv)
[
4
3
9
1
]
(v)
[
4
3
9
-2
]
Question
35
35.
Find the
multiplicative
identity of matrix A =
[
4
9
0
-9
]
(i)
[
1
0
0
3
]
(ii)
[
1
0
0
0
]
(iii)
[
1
0
0
-1
]
(iv)
[
1
0
0
2
]
(v)
[
1
0
0
1
]
Question
36
36.
Find the
multiplicative
identity of matrix A =
[
2
-3
-3
-3
-4
0
-1
-3
4
]
(i)
[
1
1
0
0
1
0
0
0
1
]
(ii)
[
1
0
0
0
1
0
0
0
-2
]
(iii)
[
1
0
0
0
3
0
0
0
1
]
(iv)
[
1
0
0
0
1
0
0
0
1
]
(v)
[
1
0
0
0
1
-1
0
0
1
]
Question
37
37.
Find the
additive
identity of matrix A =
[
-3
-3
8
-5
]
(i)
[
0
0
-2
0
]
(ii)
[
0
0
-1
0
]
(iii)
[
0
0
0
0
]
(iv)
[
0
0
1
0
]
(v)
[
0
0
2
0
]
Question
38
38.
Find the
additive
identity of matrix A =
[
3
3
0
4
3
1
-3
-4
-2
]
(i)
[
1
0
0
0
0
0
0
0
0
]
(ii)
[
0
0
0
0
0
0
0
0
0
]
(iii)
[
0
-1
0
0
0
0
0
0
0
]
(iv)
[
0
0
0
0
0
2
0
0
0
]
(v)
[
0
0
0
0
0
0
0
-2
0
]
Assignment Key
1) (iii)
2) (iii)
3) (ii)
4) (i)
5) (ii)
6) (iii)
7) (ii)
8) (iv)
9) (i)
10) (iii)
11) (ii)
12) (i)
13) (i)
14) (ii)
15) (ii)
16) (iii)
17) (iii)
18) (i)
19) (ii)
20) (ii)
21) (iii)
22) (i)
23) (ii)
24) (v)
25) (iv)
26) (v)
27) (iv)
28) (iv)
29) (ii)
30) (iii)
31) (ii)
32) (ii)
33) (iv)
34) (ii)
35) (v)
36) (iv)
37) (iii)
38) (ii)
