Question # 1

For a square matrix A, if A = At, 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

Minor of an element a_ijis denoted by

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M_ij

A_ij

|A|

None of these

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

If A = |aij| is (m x n) matrix then transpose of A is of the order

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m x m

m x n

n x n

n x m

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 matrix in which the number of rows is equal to the number of columns is called a

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Diagonal matrix

Rectangular matrix

Square matrix

Scalar matrix

For trival solution |A| is

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A

|A| = 0

A = 0

|A|≠ 0

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

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m x m

m x n

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^-1B^-1

AB^-1

A^-1B

B^-1A^-1

A diagonal matrix is always

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Identity

Triangular

Scalar

Non-singular

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a²b²c²

4a²b²c²

4abc

None

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0

1

2

3

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16

256

64

1024

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0

1

2

4

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k3

0

3k

k6

The transport of a null matrix is

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Row matrix

Column matrix

Square matrix

Null matrix

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

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A²

A³

A

None of above

(ABC)' =

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CBA'

CBA

C' B' A'

None of these

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3, -3, 11

3, 3, 11

-3, 3, -11

-3, -3, 11

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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Cofactor of an element aij denoted by Aij is

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(-2)i+j

Mij

(-1)i+j Mij

None of above

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(2x+a+b+c)

(a+b+c)

(a+b+c+x)

0

Two matrices A and B are conformable for the product AB if

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Both A and B are square

Both A and B are symmetric

Number of rows of A = number of columns of B

Number of columns of A = number of rows of B

For trival solution |A| is

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A

|A| is non zero

A = 0

None of these

Which of the following is an identity matrix?

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none of these

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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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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