Question # 1

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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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

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

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matrix

Transpose

Symmetric

Non-symmetric

The additive inverse of a matrix A is

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None of these

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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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1

0

-1

2

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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

The transpose of a zero matrix is a ______

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Column matrix

Zero matrix

Row matrix

Scalar matrix

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A

-A

A^t

A^-

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a = 4, b = 1

a = 1, b = -4

a = 0, b = 4

a = 2, b = 4

An equation of the form ax + by = k is homogeneous linear equation when:

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If order of A is m x n, then order of A^tis

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m x m

n x n

m x n

n x m

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a = 2, b = 3

a = 3, b = 2

a = 2, b = 1, 2

a = 3, b = 3

The matrix A = [aij]1xn is a

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Vector

Rectangular matrix

Column vector

Square matrix

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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0

1

-2

10

A diagonal matrix is always

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Identity

Triangular

Scalar

Non-singular

If the trace of matrix A is 5, then the trace of the matrix 3A is

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3/5

5/3

8

15

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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1

0

3

-1

If A and B are skew-symmetric then (AB)t is

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At Bt

AB

-AB

BA

A matrix with a single row is called a

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Column matrix

Row matrix

Null matrix

Identity matrix

If A is any matrix then its additive inverse is

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A

A^-1

A^t

-A

Rank of matrix [1 3 5 0] is

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1

3

2

4

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

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Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

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