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is independent of
θ
.
Solution :
Hence, Δ is independent of
θ
.
Solution :
Solution :
Solution :
Solution :
Solution :
Solution :
Solution :
Question
10. Evaluate:
Solution :
Using properties of determinants in Exercises 11 to 15, prove that:
Question
11.
Solution :
Question
12.
Solution :
Question
13.
Solution :
Question
14.
Solution :
Question
15.
Solution :
Question
16. Solve the system of the following equations: (Using matrices):
Solution :
Choose the correct answer in Exercise 17 to 19.
Question
17. If a,b,c are in A.P., then the determinant
is:
(A) 0
(B) 1
(C) x
(D) 2x
Solution :
Here, all the elements of the first row (R
1
) are zero.
Hence, we have Δ = 0.
The correct answer is A.
Question
18. If x,y,z are non-zero real numbers, then the inverse of matrix A =
is:
(A)
(B)
(C)
(D)
Solution :
Therefore, option (A) is correct.
Question
19. Let
where 0 ≤
θ
≤ 2π, Then:
(A) Det (A) = 0
Therefore, option (D) is correct.
