EXAMPLE 7 Prove that 1 b_b2 = (a - ...
Question
Fullscreen

EXAMPLE 7 Prove that 1 b_b2 = (a - b)(b -c)(c-a). 1 ca

11th - 12th Class
Maths
Solution
132
Rating
4.0 (1 ratings)
Fullscreen
sourion Let the given determinant be ( Delta ) Then, [ begin{array}{l} Delta=left|begin{array}{ccc} 1 & a & a^{2} 1 & b & b^{2} 1 & c & c^{2} end{array}right| left.begin{array}{rl} 1 & a & a^{2} 0 & b-a & b^{2}-a^{2} 0 & c-a & c^{2}-a^{2} end{array} mid text { [applying } R_{2} rightarrowleft(R_{2}-R_{1}right) text { and } R_{3} rightarrowleft(R_{3}-R_{1}right)right] end{array} ] ( =(b-a)(c-a) cdotleft|begin{array}{ccc}1 & a & a^{2} 0 & 1 & b+a 0 & 1 & c+aend{array}right| ) ( left[operatorname{taking}(b-a) text { common from } R_{2} text { and }(c-a) text { common from } R_{3}right] ) ( left.=(b-a)(c-a) times 1 cdotleft|begin{array}{cc}1 & b+a 1 & c+aend{array}right| text { [expanded by } C_{1}right] ) ( =(b-a)(c-a){(c+a)-(b+a)} ) ( =(b-a)(c-a)(c-b)=(a-b)(b-c)(c-a) ) Hence, ( Delta=(a-b)(b-c)(c-a) )
Quick and Stepwise Solutions Just click and Send Download App OVER 20 LAKH QUESTIONS ANSWERED Download App for Free