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Given A=[[2,0,-alpha],[5,alpha,0],[0,alp...

Given `A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]]` `For a in R-{a, b}`, `A^(-1)` exists and `A^(-1)=A^2-5bA + cI`, when `alpha = 1` . The value of `a +5b +c` is:

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RESONANCE ENGLISH-MATRICES & DETERMINANT-PART-II
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  2. Let A=[(0,1),(2,0)] and (A^(8)+A^(6)+A^(2)+I)V=[(32),(62)] where I i...

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  3. Let A=[3x^2 1 6x],B=[abc],a n dC=[(x+2)^2 5x^2 2x5x^2 2x(x+2)^2 2x(x+2...

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  4. Let A be an involutary matrix and S be the set containing solution of ...

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  5. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

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  6. A is a (3xx3) diagonal matrix having integral entries such that det (A...

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  7. If a(1), a(2), a(3), 5, 4, a(6), a(7), a(8), a(9) are in H.P. and the ...

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  8. If |{:(,a+b+2c,a,b),(,c,b+c+2a,b),(,c,a,c+a+2b):}|=k(alphaa+betab+gamm...

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  9. If A is a square matrix of order 3 and A' denotes transpose of matrix ...

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  10. Suppose A is a matrix such that A^2 =A and (I + A)^6 =I+ KA, then K is...

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  11. |[-bc, b^2+bc, c^2 +bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=64. t...

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  12. (i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin...

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  13. If Delta(k) = |(k,1,5),(k^(2),2n +1,2n +1),(k^(3),3n^(2),3n +1)|, " th...

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  14. The value of a for which system of equations , a^3x+(a+1)^3y+(a+2)^3z=...

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  15. Consider the system linear equations in x ,y ,a n dz given by (s in3th...

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  16. The value of k for which the set of equations 3x+ky-2z=0, x + ky + 3z ...

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  17. A(1)=[a(1)] A(2)=[{:(,a(2),a(3)),(,a(4),a(5)):}] A(3)=[{:(,a(6),a(...

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  18. If {1/2(A-A'+1)}^-1=2/lambda[(lambda-13,-lambda/3,lambda/3),(-17,10,-...

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  19. Given A=[[2,0,-alpha],[5,alpha,0],[0,alpha,3]] For a in R-{a, b}, A^(-...

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  20. Let a ,b , c be the real numbers. The following system of equations in...

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