Prove that `|{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}|` =abc `(1+(1)/(a)+(1)/(b)+(1)/(c))`

Show that {:|( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) |:}= abc ( 1+(1)/(a) +(1)/(b) +(1)/(c) ) = abc +bc +ca +ab

Prove that {:|(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

Show that |(1+a,1, 1),(1, 1+b, 1), (1, 1,1+a)|=(1)/(a)+(1)/(b)+(1)/(c )+1 .

Using properties of determinants prove that : |(1+a,1,1),( 1,1+b,1),(1,1,1+c)| =abc +bc +ca +ab

Show that |(1+a,1,1),(1,1+b,1),(1,1,1+c)| = abc(1 + 1/a + 1/b + 1/c) = abc + bc + ca + ab .

Prove that {:[(1,ab,a+b),(1,bc,b+c),(1,ca,c+a):}]=(a-b)(b-c)(c-a)

Prove that |{:(,1,a,a^(2)),(,1,b,b^(2)),(,1,c,c^(2)):}|=(a-b)(b-c)(c-a)

If a, b, c are all different from zero and Delta= |[1+a,1,1],[1,1+b,1],[1,1, 1+c]|=0 , then (1)/(a)+(1)/(b)+(1)/(c)=

Prove that |(1,1,1),(a,b,c),(a^3,b^3,c^3)| = (a - b)(b-c)(c-a)(a+b+c) .

Prove that (a, 0), (0, b), and (1, 1) are collinear if (1)/(a) + (1)/(b) = 1.