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# Matrices & Determinants - 8

M 2. Using elementary row trans formations find the inverse of the matrix A =

Sol^{n} :- A = I A

A

. R_{1} R_{1} - R_{2}

. R_{2} - 2R_{1} and R_{3} R_{3} - 3R_{1}

. R_{2} ^{1}⁄_{2} R_{2}

. R_{1} R_{1} + R_{1} and R_{3}R_{3} + 2R_{2}

. R_{3} ^{1}⁄_{2} R_{3} and .R_{1} R_{1} + ^{1}⁄_{2} R_{3} and R_{2}R_{2} - ^{1}⁄_{2} R_{3}

We get :-

A

A ^{-1} =

__M 3__ If a, b and c are P^{th}1 q^{th} and r^{th} terms of are

H.P., prove taht = 0

Solution :- A : First term, D : Common difference

1/a = A +(p -1) D, 1/b = A +(q - 1) D, 1/c = A + (r - 1)D

abc

R_{1}R_{1} - D R_{2} - (A - D)r ,

= abc = 0

__M 4 .__ for what valume of m, does the system of equation 3x + my - mand 2x - 5y = 20 lhas a solution satisfying the condstion. x > 0, y > 0.

Solution = = - (15 + 2_{m})

_{1} = - 25m 2 = 60 - 2m

X =

=> m > 30 or m < -^{15}⁄_{2}