মান নির্ণয় করো,
`abs([1+a,b,c],[a,1+b,c],[a,b,1+c])`

Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] Using the column operation C_1rarrC_1+C_2+C_3 , show that abs[A]=(a+b+c)abs[[1,b,c],[1,c,a],[1,a,b]]

|[1,1,1],[a,b,c],[bc,ca,ab]|=(a-b)(b-c)(c-a)

What is the value of abs[[a,b+c,1],[b,c+a,1],[c,a+b,1]] ?

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,ab, c]| , then

|[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,c^2]]

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Prove that: |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=|[a^2+1,b^2,c^2],[a^2,b^2+1,c^2],[a^2,b^2,c^2+1]|=1+a^2+b^2+c^2

|[bc, b+c, 1], [ca, c+a, 1], [ab, a+b, 1]|=?