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**Determinants**

**Exercise 4.1****Question 1: Evaluate the determinants in Exercises 1 and 2.**

**Answer**

= 2(−1) − 4(−5) = − 2 + 20 = 18

**Question 2: Evaluate the determinants in Exercises 1 and 2.**

**Answer**

(i) = (cos θ)(cos θ) − (−sin θ)(sin θ) = cos^{2} θ+ sin^{2} θ = 1

(ii) = (x^{2} − x + 1)(x + 1) − (x − 1)(x + 1)

= x^{3} − x^{2} + x + x^{2} − x + 1 − (x^{2} − 1)

= x^{3 }+ 1 − x^{2} + 1

= x^{3 }− x^{2} + 2

**Question 3:**

**Answer**

.

**Question 4:**

**Answer**

The given matrix is .

**Question 5: ****Evaluate the determinants**

**Answer**

(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.

**Question 6: If **

**Answer**

**Question 7: **Find values of x, if

**Answer**

**Question 8:****If , then x is equal to **

**(A) 6 **

**(B) ±6 **

**(C) −6 **

**(D) 0**

**Answer**

Answer: B

Hence, the correct answer is B.

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