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If a,b,c are all distinct and |[a,a^3,a^...

If a,b,c are all distinct and `|[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-1]|` =0, show that abc(ab+bc+ac) = a+b+c

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RESONANCE-MATRICES & DETERMINANT-HLP
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  2. If the determinant |(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h)| splits ...

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  3. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

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  4. If a,b,c are comples number and z=|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c...

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  5. If f(x)=log(10)x and g(x)=e^(ln x) and h(x)=f [g(x)], then find the va...

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  6. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

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  7. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

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  13. Let A,B,C be three 3 xx 3 matrices with real enteries. If BA+BC+AC=1, ...

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  14. If |z(1)|=|z(2)|=1"then prove that" [{:(,z(1),-z(2)),(,bar(z)(2),bar(z...

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  15. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)...

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  16. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

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  17. If the system of equations x=cy+bz, y=az+cx and z=bx+ay has a non-zero...

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  18. IfD=d i ag[d1, d2, dn] , then prove that f(D)=d i ag[f(d1),f(d2), ,f(...

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  19. Fiven the matrix A= [[-1,3,5],[1,-3,-5],[-1,3,5]] and X be the solut...

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  20. If q is a characteristic root of an singular matrix A, then prove that...

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