Question # 1

System of linear equation is inconsistent if

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System has no solution

System has one solution

System has two solution

None of above

If A = [aij]mxpand B =[aij]pxnthen order of BA is

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m x n

p x n

n x m

None of these

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Symmetric

Skew-symmetric

Hermitian

Skew hermitian

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1, 2, 3

1, 5, 9

2, 5, 8

3, 6, 9

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a = 2, b = 3

a = 3, b = 2

a = 2, b = 1, 2

a = 3, b = 3

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Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

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

Minor of an element a_ijis denoted by

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M_ij

A_ij

|A|

None of these

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Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

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-a -b -c

1

0

-1

If A = [a_ij] 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

For non-trival solution |A| is

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non zero

A = 0

|A| = 0

At = 0

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

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

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

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I

|A|

|A| I

None of these

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5

-5

none

The square matrix A is skew Hermitian when (A)'=

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A

A'

-A

A

For trival solution |A| is

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A

|A| is non zero

A = 0

None of these

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

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