Question # 1

If any two rows of a square matrix are interchanged, the determinant of the resulting matrix:

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is zero

is multiplicative inverse of the determinant of the original matrix

is additive inverse of the determinant the original matrix

none of these

A matrix of order m×1 is called:

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row matrix

column matrix

identity matrix

scalar matrix

For a square matrix A, |A| equals:

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A^t

|A^t|

-|A^t|

-A^t

The trivial solution of the homogeneous linear equations is:

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(1, 0, 0)

(0, 1, 0)

(0, 0, 1)

(0, 0, 0)

If A is a square matrix, then A - A^t is:

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[0] is a:

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scalar matrix

diagonalmatrix

lower triangularmatrix

upper triangularmatrix

The order of a matrix is shown by:

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number of columns + number of rows

number of rows × number of columns

number of columns - number of rows

If two rows (or two columns) in a square matrix are identical (i.e. corresponding elements are equal), the value of the determinant is:

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0

1

-1

±1

A^-1 exists if A is:

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singular

nonsingular

symmetric

none

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2

-2

5

-5

If A = [a_ij], B = [b_ij] and AB = 0 then:

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A = 0

B = 0

either A = 0 or B = 0

A & B not necessarily zero

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scalarmatrix

diagonalmatrix

lower triangularmatrix

uppertriangularmatrix

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None

If A is a matrix of order m × n and B is a matrix of order n × p then the order of AB is:

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p×m

p×n

n×p

m×p

Two matrices X and Y are equal if and only if:

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X and Y are of same order

Their corresponding elements are equal

Both a and b

None of these

If A and B are two matrices, then:

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A B = O

AB = BA

AB = I

AB may not be defined

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5

-5

-4

4

The additive inverse of a matrix A is:

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A

A^-1

- A

A²

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