Question # 1

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 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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a = -1/2, b = -1

a = 1, b = 2

a = 2, b = 3

None of above

Minor of an element a_ijis denoted by

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M_ij

A_ij

|A|

None of these

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

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The transpose of a row matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

Matrices are represented by

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Natural numbers

Real numbers

Small letters

Capital letters

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Zero matrix

Diagonal matrix

Column matrix

Scalar matrix

The transpose of a column matrix is a ______

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Zero matrix

Diagonal matrix

Column matrix

Row matrix

System of linear equations is inconsistent if

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System has no solution

System has one solution

System has two solution

None of above

If A is a non-singular matrix then adj A is

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Non-singular

Symmetric

Singular

Non defined

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2s²

2s³

s³

3s³

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Diagonal matrix

Scalar matrix

Triangular matrix

Identity matrix

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a = 4, b = 1

a = 1, b = -4

a = 0, b = 4

a = 2, b = 4

The matrix A = [aij]1xn is a

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Vector

Rectangular matrix

Column vector

Square matrix

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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

If A is a skew-symmetric matrix of order n and P, any square matrix of order n.prove that P' AP is

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Skew-symmetric

Symmetric

Null

Diagonal

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16

None of these

If A is singular then |A| = ______

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1

0

2

None of these

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

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BA

A²

AB

B²

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K/6

2K

3K

6K

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

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A2

A3

A

None of above

A diagonal matrix in which the diagonal elements are equal is called a

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Null matrix

Identity matrix

Scalar matrix

Row matrix

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9/4

4/9

1

None of these

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A²- 5A + 7I = 1

2A²- 3A + 7I = 0

A²- 5A + I = 0

A²- 5A + 7I = 0

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1

-1

0

I

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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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