Question # 1

Cofactor of an element aij denoted by Aij is

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(-2)i+j

Mij

(-1)i+j Mij

None of above

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0

abc

1/abc

None of these

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Hermitian matrix

Skew-hermitian matrix

Symmetric matrix

Identity matrix

A non-homogeneous linear system AX = B has no solution if

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|A| = 0

|A|≠ 0

Rank (a) = no of variables

Rank > no of variables

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I3

rI3

r

none

The transport of a rectangular matrix is a

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Square matrix

Rectangular matrix

Row matrix

Column matrix

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(2x+a+b+c)

(a+b+c)

(a+b+c+x)

0

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5

15

10

20

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

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2 AB

2 BA

A + B

AB

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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

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a = -1/2, b = -1

a = 1, b = 2

a = 2, b = 3

None of above

If A is a non singular matrix then A^-1= ______

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A matrix with a single row is called a

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Column matrix

Row matrix

Null matrix

Identity matrix

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

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16

256

64

1024

A square matrix A = [aij] is lower triangular matrix when

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aij = 0 for all i<j

bij = 0

cij = 0

dij = 0

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1

0

3

-1

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Which of the following is skew symmetric matrix

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The square matrix A is skew-symmetric when At=

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-B

-C

-A

-D

Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

An equation of the form ax + by = k is homogeneous linear equation when

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b = 0, a = 0

a = 0,b ≠ 0

b = -0,a≠ 0

a≠ 0,b≠ 0, k = 0

For non-trival solution |A| is

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A = 0

A^t= 0

|A| = 0

None of these

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2 x 2

2 x 3

3 x 2

3 x 3

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If A = |aij| is (m x n) matrix then transpose of A is of the order

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m x m

m x n

n x n

n x m

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Null matrix

Triangular matrix

Unit matrix

Rectangular matrix

If A is a non-singular matrix then adj A is

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Non-singular

Symmetric

Singular

Non defined

A and B be two square matrices and if their inverse exist, the (AB)^-1=

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A^-1B^-1

AB^-1

A^-1B

B^-1A^-1

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3, -3, 11

3, 3, 11

-3, 3, -11

-3, -3, 11

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