Matrix MCQ - 2 - Mathematics MCQ

4

6

8

12

A real number

Either a real or a complex number

An arrangement of mn numbers, over the given set S, in a rectangular array of m rows and n Columns.

Same as determinant

Natural numbers

Integers

Real numbers

Complex number

iderapotent 

nilpotent

Involutory

periodic

Row vectors 

Column vectors 

Null matrices

Scalar matrices

none of these

Null matrix

Scalar matrix

Unit matrix

Skew symmetric matrix

has rank zero

has rank 1

is orthogonal

has rank n

The first row and the first column of the given matrix

Any number of rows and one column of the given matrix

One row and any number of columns of the given matrix

Any number of rows and any number of columns of the given matrix

consistent having a unique solution

consistent having many solution

inconsistent having no solution

All of the above

Number of rows in A is equal to the number of columns in B

Number of columns in A is equal to the number of rows in B

Number of rows and columns in A is equal to the number of rows and columns in B

None of the above

For a homogeneous n x n system of linear equations (A - λI)X = 0 having a non - trivial solution when the rank of (A - λI) is less than n

For matrix A^m, m being a positive integer, (λ_i^m x^mi) will be the eigen pair for all i.

If A^T = A^-1, then |λ_i | = 1 for all i

If A^T = A, then λ_i is real for all i

None of these

1 and 25

6 and 4

5 and 1

2 and 10

x ( x -1)

x (x + 1 )

x ( 1 - x)

x ²( 1+ x)

(x—1 ) ( x + 1)

x(x —1)

x(1 —x)

 x + 1

2 x 3

3 x 2

2 x 2

3 x 3

P₁₁P₂₂ — P₁₂P₂₁ = 1

P₁₁P₂₂ — P₁₂ P₂₁ = —1

P₁₁P₂₂ - P₁₂ P₂₁ = 0

P₁₁P₂₂ + P₁₂ P₂₁ = 0

Augmented matrix [P q] must have the same rank as matrix P

Vector q must have only non — zero elemetns

Matrix P must be singular

Matrix P must be square

D₁D₂ is a diagonal matrix 

D₁D₂ = D₂D₁ 

 is a diagonal matrix

All of these

Neither associative nor commutative

Commutative but not associative 

Associative as well as commutative

Associative but not commutative

1

2

n

Depends on 'a'

0,+1, —1

1, -1, 1

i, - i , 1

i, - i , 0

The interchange of two rows or columns

The multiplication of a row or a column by any real number

The addition of a multiple of one row or column to another row or column

The multiplication of a row or a column by any non — zero number

A must be a sqare matrix

a_ij = 0 for all i > j

It is not necessary that the elements a_ij ≠ 0 for all i ≤ j 

The elements in the principal diagonal are necessarily zero.

A number r is said to be the rank of the matrix A if every minor of order (r + 1) vanishes

A number r is said to be the rank of the matrix A if there exists at least one minor of order r which does not vanish

A number r is said to be the rank of the matrix A if there exists at least one minor of order r which does not vanish and every minor of order (r + l)vanishes

A number r is said to be the rank of the matrix A if the determinant of any r x r sub matix of A is non — zero

a = b = c

a, b, c are all different but a + b + c = 0

Two of the numbers a, b, c are equal but are different from the third

a, d, c are all different and a + b + c ≠ 0

AB = BA

AB² = A²B

AB = -BA

A/B = B/A