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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