" (ii) "|[2,a,abc],[2,b,bca],[2,c,cab]|

The value of the det. |[2,a,abc],[2,b,bca],[2,c,cab]| is

det[[2,a,abc2,b,bca2,c,cab]]

Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(2,c,cab)|

Identify the like terms in the following: (i) a^(2), b^(2), - 2a^(2) , c^(2) , 4a (ii) 3x, 4xy, - yz, (1)/(2)zy (iii) -2xy^(2), x^(2) y, 5y^(2)x, x^(2) z (iv) 'abc, ab^(2)c, abc^(2), c^(2)ab, b^(2)ac, a^(2)bc, cab^(2)

Show that , |[(a^2+b^2)/c,c,c],[a,(b^2+c^2)/a,a],[b,b,(c^2+a^2)/b]|=4abc

If =det[[abc,b^(2)c,c^(2)babc,c^(2)a,ca^(2)abc,c^(2)a,ca^(2)abc,a^(2)b,b^(2)a]]=0,(a,b,c in R) and a+b+c,=0a+b+c,=0

Identify the like terms in each of the following: -2x^(2)y,x^(2)z,-yx^(2),x^(2)y^(2)cab^(2),a^(2)bc,b^(2)ac,c^(2)ab,ab^(2)c,abc,acb^(2)

" if " Delta = |{:(abc,,b^(2)c,,c^(2)b),(abc ,,c^(2)a,,ca^(2)),( abc,,a^(2)b,,b^(2)a):}| =0 , (a, b, c in R " and are all " different and non- zero ) the prove that a+b+c=0