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Exercise - 4.2

Question-1 :-  Using the property of determinants and without expanding, prove that:

Solution :-

Question-2 :-  Using the property of determinants and without expanding, prove that:

Solution :-

Question-3 :-  Using the property of determinants and without expanding, prove that:

Solution :-

Question-4 :-  Using the property of determinants and without expanding, prove that:

Solution :-

Question-5 :-  Using the property of determinants and without expanding, prove that:

Solution :-

Question-6 :-  Using the property of determinants and without expanding, prove that:

Solution :-

Question-7 :-  Using the property of determinants and without expanding, prove that:

Solution :-

Question-8 :-  Using the property of determinants, prove that:

Solution :-
(i)

(ii)

Question-9 :-  Using the property of determinants, prove that:

Solution :-

Question-10 :-  Using the property of determinants, prove that:

Solution :-
(i)

(ii)

Question-11 :-  Using the property of determinants, prove that:

Solution :-
(i)

(ii)

Question-12 :-  Using the property of determinants, prove that:

Solution :-

Question-13 :-  Using the property of determinants, prove that:

Solution :-

Question-14 :-  Using the property of determinants, prove that:

Solution :-

Question-15 :-  Let A be a square matrix of order 3 × 3, then |kA| is equal to
(A) k|A|   (B) k²|A|   (C) k3|A|   (D) 3k|A|

Solution :-
A is a square matrix of order 3 × 3.

The correct answer is C.

Question-16 :-  Which of the following is correct
(A) Determinant is a square matrix.
(B) Determinant is a number associated to a matrix.
(C) Determinant is a number associated to a square matrix.
(D) None of these

Solution :-
We know that to every square matrix, A = [aij] of order n.
We can associate a number called the determinant of square matrix A, where aij = (i, j)th element of A.
Thus, the determinant is a number associated to a square matrix.
The correct answer is C.

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