Question # 1

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

The order of the matrix [1 2 3] is

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1 x 1

3 x 3

3 x 1

1 x 3

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A(α) - A(β)

A(α) + A(β)

A(α-β)

A(α+β)

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An upper triangular matrix

A lower triangular matrix

A diagonal matrix

A null matrix

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

For trival solution |A| is

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A

|A| = 0

A = 0

|A|≠ 0

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3, -3, 11

3, 3, 11

-3, 3, -11

-3, -3, 11

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

Matrices are represented by

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Natural numbers

Real numbers

Small letters

Capital letters

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Identity matrix

Diagonal matrix

Null matrix

Hermitian matrix

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1

-1

0

I

Every identity matrix is

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Row-vector

Scalar

Column-vector

All

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

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A²

A³

A

None of above

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2

4

6

8

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The matrix A is Hermitian when (A)' =

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A

-A

A

A'

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

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(2x4)

(2x7)

(2x3)

(7x2)

For a square matrix A, if A = At, then A is called

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Matrix

Transpose

Symmetric

Non-symmetric

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

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

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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Orthogonal

Involutary

Idempotent

Nilpotent

The square matrix A is skew-symmetric when At=

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-B

-C

-A

-D

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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K/6

2K

3K

6K

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

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BA

A²

AB

B²

The transport of a rectangular matrix is a

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Square matrix

Rectangular matrix

Row matrix

Column matrix

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

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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A

-A

A^t

A^-

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