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Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x)...

Let `A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]`then prove that `A^(-1)` exists if `3x+lambda ne0, lambda=ne0`

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RESONANCE-MATRICES & DETERMINANT-HLP
  1. If a,b,c are comples number and z=|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c...

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

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

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  5. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

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  6. Let 'A' is (4xx4) matrix such that the sum of elements in each row is ...

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  7. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

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  8. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

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  9. Let p and q be real number such that x^(2)+px+q ne0 for every real num...

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

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

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

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

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

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

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

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  18. If there are three square matrix A, B, C of same order satisfying the...

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  19. If A is non-singular matrix satifying AB-BA=A, then prove that det(B+I...

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  20. If a rank is a number associated with a matrix which is the highest or...

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