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Evaluate the determinants
(i) 
(ii) 
(i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos2θ+ sin2θ = 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
If
, then show that
The given matrix is.
It can be observed that in the first column, two entries are zero. Thus, we expand along the first column (C1) for easier calculation.
From equations (i) and (ii), we have:
Hence, the given result is proved.
Evaluate the determinants
(i) 
(iii) 
(ii) 
(iv) 
(i) Let
.
It can be observed that in the second row, two entries are zero. Thus, we expand along the second row for easier calculation.
(ii) Let
.
By expanding along the first row, we have:
(iii) Let
By expanding along the first row, we have:
(iv) Let
By expanding along the first column, we have:
If
, then x is equal to
(A) 6 (B) ±6 (C) −6 (D) 0
Answer: B
Hence, the correct answer is B.
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, then show that
, find
.
