Question # 1

The transpose of a zero matrix is a ______

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Column matrix

Zero matrix

Row matrix

Scalar matrix

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0

1

2

3

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Symmetric

Skew-symmetric

Hermitian

Skew hermitian

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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16

None of these

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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Singular

Non-singular

Adjoint

None of above

For non-trival solution |A| is

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non zero

A = 0

|A| = 0

At = 0

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

For trival solution |A| is

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A

|A| = 0

A = 0

|A|≠ 0

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

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Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

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

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cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

Let A be a square matrix. Then, 1/2 (A-A') is

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Skew-symmetric

Symmetric

Null

None of the above

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

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Non-singular

Symmetric

Singular

Non defined

(ABC)' =

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CBA'

CBA

C' B' A'

None of these

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Identity matrix

Diagonal matrix

Null matrix

Hermitian matrix

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0

abc

1/abc

None of these

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The transpose of a row matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

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BA

A²

AB

B²

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(2x+a+b+c)

(a+b+c)

(a+b+c+x)

0

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0

1

-2

10

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3, -3, 11

3, 3, 11

-3, 3, -11

-3, -3, 11

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3 x 2

2 x 3

3 x 3

2 x 2

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I

|A|

|A| I

None of these

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3K

K2

K3

K

In order of A is m x n and order of B is n x p then order of AB is

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m x m

n x n

m x p

p x m

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