Q9 of 26 Page 1

If x, y, z are in GP, then using properties of determinants, show that , where x ≠ y ≠ z and p is any real number.

Given: x, y, z are in G.P


To show:


Proof:



C1→ C1 – pC2 – C3





Expanding by R3


Δ = (-p2y – 2py – z)(xz – y2) …(i)


Since, x, y, z are in G.P. This means



⇒ y2 = xz


⇒ y2 – xz = 0


or xz – y2 = 0


Substituting the value in eq. (i), we get


Δ = (-p2y – 2py – z)(0)


⇒ Δ = 0


∴ LHS = RHS


Hence Proved


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To raise money for an orphanage, students of three schools A, B and C organized an exhibition in their locality, where they sold paper bags, scrap-books and pastel sheets made by them using recycled paper, at the rate of Rs. 20, Rs.15 and Rs. 5 per unit respectively. School A sold 25 paper-bags 12 scrap-books and 34 pastel sheets. School B sold 22 paper-bags, 15 scrapbooks and 28 pastel-sheets while school C sold 26 paper-bags, 18 scrap-books and 36 pastel sheets. Using matrices, find the total amount raised by each school.

By such exhibition, which values are inculcated in the students?


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Let , then show that A2 – 4A + 7I = O.

Using this result calculate A3 also.


OR


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Evaluate:

OR


Evaluate: