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Determinants Ex-4.1 Questions Answers

Subjects

Question 1 :

Evaluate thedeterminants in Exercises 1 and 2.

Answer 1 :



Solution

 = 2(−1) − 4(−5) =− 2 + 20 = 18

Question 2 :

.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.


Selected

 

Determinants Ex-4.1 Contributors

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