Chapter 4 Determinants Ex 4.1 Solutions
Question - 1 : - Evaluate thedeterminants in Exercises 1 and 2.
Answer - 1 : -
Solution
= 2(−1) − 4(−5) =− 2 + 20 = 18
.Evaluate thedeterminants in Exercises 1 and 2.
Answer - 2 : -
(i) 
(ii) 
Solution
(i) = (cos θ)(cos θ)− (−sin θ)(sin θ) = cos2 θ+ sin2 θ = 1
(ii)
= (x2 − x + 1)(x + 1) − (x −1)(x + 1)
= x3 − x2 + x + x2 − x + 1 − (x2 − 1)
= x3 + 1 − x2 + 1
= x3 − x2 + 2
Question - 3 : - If
, then show that
Answer - 3 : -
The given matrix is
Question - 4 : - If
, then show that
Answer - 4 : -
The given matrix is
It can be observed thatin the first column, two entries are zero. Thus, we expand along the firstcolumn (C1) for easier calculation.
From equations (i) and(ii), we have:
Hence, the given resultis proved.
Question - 5 : - Evaluate thedeterminants
Answer - 5 : -
(i) 
(iii) 
(ii) 
(iv) 
Solution
(i) Let
It can be observed thatin the second row, two entries are zero. Thus, we expand along the second rowfor easier calculation.
(ii) Let
By expanding along thefirst row, we have:
(iii) Let
By expanding along thefirst row, we have:
(iv) Let
By expanding along thefirst column, we have:
Question - 6 : - If
, find
Answer - 6 : -
Let
By expanding along thefirst row, we have:
Question - 7 : - Find values of x, if
(i) 
(ii) 
Answer - 7 : -
(i)
(ii)
Question - 8 : - If
, then x is equalto
(A) 6 (B) ±6 (C) −6 (D)0
Answer - 8 : -
Hence, the correctanswer is B.