Question # 1

A diagonal matrix is always

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Identity

Triangular

Scalar

Non-singular

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

The matrix A = [aij]mxn with m≠n is

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Rectangular

Symmetric

Square

None

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0

1

2

3

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1, 2, 3

1, 5, 9

2, 5, 8

3, 6, 9

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-3

-7

1

0

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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

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Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

(ABC)' =

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CBA'

CBA

C'B'A

C'B'A'

Trival solution of homogeneous linear equation is

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(0, 0, 0)

(1, 2, 3)

(1, 3, 5)

a, b and c

Matrices are represented by

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Natural numbers

Real numbers

Small letters

Capital letters

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

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matrix

Transpose

Symmetric

Non-symmetric

A = [3] is a/an

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Square matrix

Scalar matrix

Diagonal matrix

Identity matrix

The additive inverse of a matrix A is

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None of these

If A is any matrix then its additive inverse is

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A

A^-1

A^t

-A

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2 x 2

2 x 3

3 x 2

3 x 3

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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

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

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 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

Minor of an element a_ijis denoted by

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M_ij

A_ij

|A|

None of these

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Scalar matrix

Identity matrix

Null matrix

Symmetric 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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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

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

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9/4

4/9

1

None of these

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all are correct

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