Question # 1

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 is non singular matrix then A^t is:

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singular

nonsingular

symmetric

none

If A is a square matrix, then:

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|A^t| = A

|A^t| = -A

|A^t| = |A|

A^t= A

For a square matrix A, |A| equals:

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A^t

|A^t|

-|A^t|

-A^t

If A is a square matrix order 3 × 3 the |kA| equals:

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k |A|

k²|A|

k³ |A|

k⁴ |A|

If the matrices A & B have the orders 2×3 and 5×2 then order BA is:

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3×5

5×2

2×2

none

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diagonal matrix

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singular

non-singular

rectangular

null

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3×1

1×3

3×3

1×1

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1

-5

-1

none

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If A = [aij] and B = [bij] are two matrices of same order r × s, then order of A - B is:

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r - s

r × s

r + s

none of these

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1

-1

-6

6

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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3×2

2×3

2×2

3×3

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

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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)

A matrix of order m×1 is called:

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row matrix

column matrix

identity matrix

scalar matrix

If each element of a 3 × 3 matrix A is multiplied by 3, then the determinant of the resulting matrix is:

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|A|³

27|A|

3|A|

9|A|

Minors and co-factors of the elements in a determinant are equal in magnitude but they may differ in:

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order

position

sign

symmetry

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