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**Determinants**

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

**Answer**

= 2(âˆ’1) âˆ’ 4(âˆ’5) = âˆ’ 2 + 20 = 18

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

**Answer**

(i) = (cos Î¸)(cos Î¸) âˆ’ (âˆ’sin Î¸)(sin Î¸) = cos^{2} Î¸+ sin^{2} Î¸ = 1

(ii) = (x^{2} âˆ’ x + 1)(x + 1) âˆ’ (x âˆ’ 1)(x + 1)

= x^{3} âˆ’ x^{2} + x + x^{2} âˆ’ x + 1 âˆ’ (x^{2} âˆ’ 1)

= x^{3 }+ 1 âˆ’ x^{2} + 1

= x^{3 }âˆ’ 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) Â±6 **

**(C) âˆ’6 **

**(D) 0**

**Answer**

Answer: B

Hence, the correct answer is B.

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