Q. 264.3( 3 Votes )

# Using properties

Answer : To prove: triangle ABC is isosceles      Similarly,  Taking (cos B – cos A) and (cos C – cos A) common from C2 and C3 respectively  Expanding the determinant along R1:   One term out of the three must be zero

Therefore, either cos C = cos A or cos B = cos A or cos C = cos B

either AB = BC or AC = BC or AB = AC

triangle ABC is an isosceles triangle

Hence Proved

OR

Given: There are 3 types of pen namely ‘A’ ‘B’ and ‘C’. Meenu, Jeevan and Shikha have purchased different number of these pens

To find: cost of each variety of pen

Let cost of pen of variety ‘A’, ‘B’ and ‘C’ be p, q and r respectively

According to the question:

p + q + r = 21

4p + 3q + 2r = 60

6p + 2q + 3r = 70

To solve these equations and get values of p, q and r, we have:

AX = B where,  Now, check whether system has unique solution or not: = 1{3×3 – 2×2} – 1{3×4 – 2×6} + 1{4×2 – 3×6}

= 1(9 – 4) – 1(12 – 12) + 1{8 – 18}

= 1(5) – 1(0) + 1(-10)

= 5 – 0 – 10

= –5 The system of the equation is consistent and have unique solution

AX = B

X = A-1 B

Formula used:                      Thus,  X = A-1 B      Therefore,

Cost of pen of variety ‘A’, ‘B’ and ‘C’ are Rs. 5, Rs. 8 and Rs. 8 respectively.

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