Question # 1

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3 x 2

2 x 3

3 x 3

2 x 2

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

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A

A'

-A

A

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-3

-7

1

0

If A and B are skew-symmetric then (AB)t is

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At Bt

AB

-AB

BA

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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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0

Independent of a

Independent of b

Independent of c

For non-trival solution |A| is

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A = 0

A^t= 0

|A| = 0

None of these

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0

1

2

3

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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Every identity matrix is

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Row-vector

Scalar

Column-vector

All

If A is any matrix then its additive inverse is

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A

A^-1

A^t

-A

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Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

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

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all

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(ABC)' =

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CBA'

CBA

C'B'A

C'B'A'

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An upper triangular matrix

A lower triangular matrix

A diagonal matrix

A null 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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Triangular matrix

Identity matrix

Diagonal matrix

Scalar matrix

Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

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all are correct

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

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A-1 B-1

AB-1

A-1B

B-1A-1

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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

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a.b and c

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-a -b -c

1

0

-1

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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