सकराता कि हम 1bb-a-b/b-CER)

By using properties of determinants. Show that: (i) |1a a^2 1bb^2 1cc^2|=(a-b)(b-c)(c-a) (ii) |1 1 1a b c a^3b^3c^3|=(a-b)(b-c)(c-a)(a+b+c)

Prove that =|a cc-a a+cc bb-c b+c a-bb-c0a-c x y z1+x+y|=0 implies that a ,b ,c are in A.P. or a ,c ,b are in G.P.

The value of determinant |a-bb-cc-a b-cc-a a-b c-a a-bb-c| is equal to- a b c b. 2a b c c. 0 d. none

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is |a-c-b-c b-a-b-a c| (b) |a b c b c a c a b| |a c bb a cc b a| (d) |a a+bb+c bb+cc+a cc+a a+b|

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is |a-c-b-c b-a-b-a c| (b) |a b c b c a c a b| |a c bb a cc b a| (d) |a a+bb+c bb+cc+a cc+a a+b|

a +b , b+ c 1- ab 1- bc o b, are in For a, b, CER1O), let AP. If ?, ? are the roots of the quadratic equation 2acx2 + 2abcx + (a + c) 0, then the value of 1 + ?)(1 + ?) is

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=0

Without expanding, show that the value of each of the following determinants is zero: |1//a , a^2b c1//bb^2a c1//cc^2a b| (ii) |a+b2a+b3a+b2a+b3a+b4a+b4a+b5a+b6a+b| (iii) |1a a^2 1bb^2 1cc^2\ \ \ -b c-a c-a b|

- aa bc a - b - c - - bb - c - c