Question # 1

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a.b and c

If the trace of matrix A is 5, then the trace of the matrix 3A is

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3/5

5/3

8

15

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

For a square matrix A, if A = A^t, then A is called

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matrix

Transpose

Symmetric

Non-symmetric

For non-trival solution |A| is

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A = 0

A^t= 0

|A| = 0

None of these

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

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A2

A5

A3

A7

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3 x 1

1 x 3

3 x 3

1 x 1

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2

4

6

8

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Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

If for the matrix A,A5 = 1,then A-1=

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A2

A3

A

None of above

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-a -b -c

1

0

-1

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16

None of these

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The matrix A is Hermitian when (A)' =

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A

-A

A

A'

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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If there are m rows and n columns in a matrix then its order is

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m x n

m x m

n x n

n x m

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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1

-1

0

I

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

If A is singular then |A| = ______

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1

0

2

None of these

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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 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

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1, 2, 3

1, 5, 9

2, 5, 8

3, 6, 9

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x =0, y =4

x = -1, y = 2

x = 2, y = 3

x = 3, y = 4

The transport of a null matrix is

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Row matrix

Column matrix

Square matrix

Null matrix

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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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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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