Question # 1

The transpose of a column matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

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A(α) - A(β)

A(α) + A(β)

A(α-β)

A(α+β)

(ABC)' =

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CBA'

CBA

C' B' A'

None of these

The square matrix A is skew-symmetric when At =

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-B

-C

-A

-D

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1

0

-1

2

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1, 2, 3

1, 5, 9

2, 5, 8

3, 6, 9

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3 x 2

2 x 3

3 x 3

2 x 2

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(2x+a+b+c)

(a+b+c)

(a+b+c+x)

0

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K/6

2K

3K

6K

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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

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

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Symmetric

Hermition

Skew-symmetric

None

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4A - 3I

3A - 4I

A - I

None of these

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Symmetric

Skew-symmetric

Hermitian

Skew hermitian

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

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3K

K2

K3

K

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Singular

Non-singular

Adjoint

None of above

The transport of a square matrix is a

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Row matrix

Column matrix

Square matrix

Null matrix

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2 x 2

2 x 3

3 x 2

3 x 3

If A is a non singular matrix then A^-1= ______

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

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matrix

Transpose

Symmetric

Non-symmetric

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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Square matrix

Row matrix

Symmetric matrix

Null matrix

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

For non-trival solution |A| is

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A = 0

A^t= 0

|A| = 0

None of these

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

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Non-singular

Symmetric

Singular

Non defined

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^-

A^t

-A

A

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

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At Bt

AB

-AB

BA

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