15. Using properties of determinants, prove the following b+c c+a a+ b

15.Using properties of determinants,prove the following b+c+aa+b

Using properties of determinants, prove the following : |[a, a^2,bc],[b,b^2,ca],[c,c^2,ab]|=(a-b)(b-c)(c-a)(b c+c a+a b)

15.Using properties of determinants,prove the following det[[a-b,b-c,c-ab+c,c+a,a+b]]=a^(3)+b^(3)+c^(3)-3abc,]|=

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

Using the properties of determinants, prove the following |{:(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c):}|=(a+b+c)(a^2+b^2+c^2)

Using properties of determinants prove the following. abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc

Using properties of determinants, prove the following: |3"a"-"a"+"b"-"a"+"c""a"-"b"3"b""c"-"b""a"-"c""b"-"c"3"c"|=3("a"+"b"+"c")("a b"+"b c"+"c a")