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Mathematics ECAT Pre Engineering Chapter 5 Matrices and Determinants Online Test MCQs With Answers
Question # 1
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all
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Question # 2
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Orthogonal
Involutary
Idempotent
Nilpotent
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Question # 3
Cofactor of an element a
ij
is defined by
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(-1)
i+j
|A|
(-1)
i+j
M
ij
(-1)
i+j
M
-1
None of these
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Question # 4
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6, -12, -18
-6, 4, 9
-6, -4, -9
-6, 12, 18
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Question # 5
A diagonal matrix in which the diagonal elements are equal is called a
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Null matrix
Identity matrix
Scalar matrix
Row matrix
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Question # 6
If A is a skew-symmetric matrix of order n and P, any square matrix of order n.prove that P' AP is
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Skew-symmetric
Symmetric
Null
Diagonal
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Question # 7
A square matrix all of whose elements except the main diagonal are zeros is called a
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Null matrix
Singular matrix
Symmetric matrix
Diagonal matrix
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Question # 8
If A and B are skew-symmetric then (AB)t is
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At Bt
AB
-AB
BA
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Question # 9
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A
2
- 5A + 7I = 1
2A
2
- 3A + 7I = 0
A
2
- 5A + I = 0
A
2
- 5A + 7I = 0
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Question # 10
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I
14 I
0
None of these
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Question # 11
The order of the matrix [1 2 3] is
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1 x 1
3 x 3
3 x 1
1 x 3
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Question # 12
The transpose of a row matrix is a ______
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Zero matrix
Diagonal matrix
Column matrix
Row matrix
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Question # 13
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a = -1/2, b = -1
a = 1, b = 2
a = 2, b = 3
None of above
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Question # 14
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x =0, y =4
x = -1, y = 2
x = 2, y = 3
x = 3, y = 4
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Question # 15
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Identity matrix
Diagonal matrix
Null matrix
Hermitian matrix
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Question # 16
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Question # 17
(ABC)' =
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CBA'
CBA
C'B'A
C'B'A'
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Question # 18
If the trace of matrix A is 5, then the trace of the matrix 3A is
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3/5
5/3
8
15
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Question # 19
The transpose of a zero matrix is a ______
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Column matrix
Zero matrix
Row matrix
Scalar matrix
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Question # 20
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1
0
-1
2
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Question # 21
For any positive integer n
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ABn = Bn A ⇔ AB = BA
ABn = Bn A⇔ A,B are square matrices and AB = BA
ABn = BnA⇔ A + B
ABn = BnA ⇔ A and B are square matries
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Question # 22
If for the matrix A,A5 = 1,then A-1=
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A2
A3
A
None of above
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Question # 23
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Question # 24
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Symmetric
Skew-symmetric
Hermitian
Skew hermitian
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Question # 25
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Question # 26
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Question # 27
If A and B are two matrices such that AB = B and BA =A, then A
2
+ B
2
=
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2 AB
2 BA
A + B
AB
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Question # 28
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2s
2
2s
3
s
3
3s
3
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Question # 29
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0
1
-2
10
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Question # 30
If for the matrix A, A
5
= I, then A
-1
=
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A
2
A
3
A
None of above
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Question # 31
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3 x 2
2 x 3
3 x 3
2 x 2
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