Question # 1

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a = 2, b = 3

a = 3, b = 2

a = 2, b = 1, 2

a = 3, b = 3

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

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matrix

Transpose

Symmetric

Non-symmetric

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6, -12, -18

-6, 4, 9

-6, -4, -9

-6, 12, 18

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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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

The transport of a null matrix is

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Row matrix

Column matrix

Square matrix

Null matrix

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x =0, y =4

x = -1, y = 2

x = 2, y = 3

x = 3, y = 4

The transpose of a zero matrix is a ______

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Column matrix

Zero matrix

Row matrix

Scalar matrix

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

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2

4

6

8

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

If A is singular then |A| = ______

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1

0

2

None of these

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

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A

A'

-A

A

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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5

-5

none

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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0

1

2

3

A square matrix A = [aij] is upper triangular when

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cij = 0

bij = 0

aij = 0 for all i > j

dij = 0

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(2x+a+b+c)

(a+b+c)

(a+b+c+x)

0

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Hermitian matrix

Skew-hermitian matrix

Symmetric matrix

Identity matrix

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k3

0

3k

k6

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Orthogonal

Involutary

Idempotent

Nilpotent

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Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

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BA

A²

AB

B²

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

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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

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Symmetric

Skew-symmetric

Hermitian

Skew hermitian

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