Question # 1

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 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

If A is a matrix of order m × n, then the number of elements in each row of A is:

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m

n

m + n

m - n

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

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diagonal matrix

If A is non singular matrix then A^t is:

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singular

nonsingular

symmetric

none

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 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|

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2

-2

5

-5

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singular

non-singular

rectangular

null

If A is a square matrix, then:

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|A^t| = A

|A^t| = -A

|A^t| = |A|

A^t= 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

The additive inverse of a matrix A is:

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A

A^-1

- A

A²

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scalar matrix

diagonalmatrix

triangularmatrix

none of these

A matrix in which each element is 0 is called:

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scalar matrix

diagonalmatrix

lower triangularmatrix

upper triangularmatrix

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

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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

A^-1 exists if A is:

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singular

nonsingular

symmetric

none

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zero

non-singular

singular

none of these

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diagonal matrix

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