If `|[1,a,bc] , [1,b,ac] , [1,c,ab]|=lambda|[a^2,b^2,c^2] , [a,b,c] , [1,1,1]|` then `lambda` i...

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Let B=[1 3 1 5] and A be a 2*2 Matrix such that AB^-1=A^-1. If BCB^-1=A and C^4+aC^2+BI=0, then 2B-a Let B=[1 3 1 5] and A be a 2*2 Matrix such that AB^-1=A^-1. If BCB^-1=A and C^4+aC^2+BI=0, then 2B-a
The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^... The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^...
Show that `|(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)` Show that `|(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)`
Show without expanding at any stage that: ` | [1,bc, a(b+c)],[1,ca, b(c+a)],[1,ab, c(a+b)]|=0 ` Show without expanding at any stage that: ` | [1,bc, a(b+c)],[1,ca, b(c+a)],[1,ab, c(a+b)]|=0 `
Show that ` |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a) ` Show that ` |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a) `
If 1/a + 1/c + 1/(a-b) + 1/(c-b) = 0, prove that a, b, c are in HP unless b = a + c. If 1/a + 1/c + 1/(a-b) + 1/(c-b) = 0, prove that a, b, c are in HP unless b = a + c.
Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)| | 12 | DETERMINANTS... Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c,c^2)| | 12 | DETERMINANTS...
Q63 | If abc=1, prove that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1 Q63 | If abc=1, prove that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1