Question # 1

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1

0

3

-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

If there are m rows and n columns in a matrix then its order is

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m x n

m x m

n x n

n x m

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Scalar matrix

Identity matrix

Null matrix

Symmetric matrix

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2 x 2

2 x 3

3 x 2

3 x 3

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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Identity matrix

Diagonal matrix

Null matrix

Hermitian matrix

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Null matrix

Triangular matrix

Unit matrix

Rectangular matrix

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Orthogonal

Involutary

Idempotent

Nilpotent

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

The transpose of a zero matrix is a ______

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Column matrix

Zero matrix

Row matrix

Scalar matrix

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1

-1

0

I

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16

256

64

1024

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Symmetric

Skew-symmetric

Hermitian

Skew hermitian

For non-trival solution |A| is

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non zero

A = 0

|A| = 0

At = 0

Every identity matrix is

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Row-vector

Scalar

Column-vector

All

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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

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

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

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Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

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BA

A²

AB

B²

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

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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An upper triangular matrix

A lower triangular matrix

A diagonal matrix

A null matrix

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a²b²c²

4a²b²c²

4abc

None

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