Question # 1

Matrix multiplication is

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Commutative

Not commutative

Not associative

Not distributive

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0

1

2

4

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I

|A|

|A| I

None of these

The square matrix A is skew-symmetric when At=

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-B

-C

-A

-D

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

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1 x 1

1 x 10

10 x 10

10 x 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

A square matrix A for which A^t= -A is called a

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Column matrix

Symmetric matrix

Skew-symmetric matrix

Row 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

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Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

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0

1

-2

10

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5

15

10

20

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A^-

A^t

-A

A

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0

1

-A

-1

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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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The square matrix A is skew-symmetric when At =

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-B

-C

-A

-D

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

Which of the following is skew symmetric matrix

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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

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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a = 2, b = 3

a = 3, b = 2

a = 2, b = 1, 2

a = 3, b = 3

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a, b and c

A non-homogeneous linear system AX = B has no solution if

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|A| = 0

|A|≠ 0

Rank (a) = no of variables

Rank > no of variables

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-3

-7

1

0

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2

4

6

8

The transport of a square matrix is a

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Row matrix

Column matrix

Square matrix

Null matrix

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all are correct

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