Question # 1

Cofactor of an element a_ijis defined by

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(-1)^i+j|A|

(-1)^i+jM_ij

(-1)^i+jM^-1

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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3 x 2

2 x 3

3 x 3

2 x 2

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

A square matrix A for which A^t= -A is called a

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Column matrix

Symmetric matrix

Skew-symmetric matrix

Row matrix

The order of the matrix A is 3 x 2 and that of B is 2 x 3. The order of the matrix BA is

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3 x 3

3 x 2

2 x 5

5 x 2

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5

-5

none

For non-trival solution |A| is

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A = 0

A^t= 0

|A| = 0

None of these

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a = 2, b = 3

a = 3, b = 2

a = 2, b = 1, 2

a = 3, b = 3

The square matrix A is skew-symmetric when At =

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-B

-C

-A

-D

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

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2 x 3

3 x 2

2 x 5

5 x 2

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2 x 2

2 x 3

3 x 2

3 x 3

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5

15

10

20

The transpose of a column matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

(ABC)' =

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CBA'

CBA

C' B' A'

None of these

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16

None of these

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Zero matrix

Diagonal matrix

Column matrix

Scalar matrix

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A

-A

A^t

A^-

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A^-

A^t

-A

A

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

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Skew-symmetric

Symmetric

Null

None of the above

The matrix A = [aij]mxn with m ≠n is always

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Symmetric

Hermition

Skew-symmetric

None

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2

4

6

8

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

For a square matrix A, if A = At, then A is called

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Matrix

Transpose

Symmetric

Non-symmetric

Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

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

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

The number of non zero rows in echelon form of a matrix is called

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Order of matrix

Rank of matrix

Row operation

None of these

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0

1

-A

-1

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