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Which of the following is true for matro...

Which of the following is true for matrox `A=[{:(,1,-1),(,2,3):}]`

A

`A+4I` is a symmetric matrix

B

`A^(2)-4A+5I_(2)=0`

C

A-B is a diagonal matrix for any value of `alpha "if" =[{:(,alpha,-1),(,2,5):}]`

D

A-4I is a skew symmetric matrix.

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The correct Answer is:
B, C
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RESONANCE-MATRICES & DETERMINANT-PART-III

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  3. Which of the following is true for matrox A=[{:(,1,-1),(,2,3):}]

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  4. Suppose a(1),a(2),a(3) are in A.P. and b(1),b(2),b(3) are in H.P. and ...

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  5. Let theta=(pi)/(5),X=[{:(,cos theta,-sin theta),(,sin theta,cos theta)...

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  6. If Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}|,then

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  7. Let a.b ,gt 0 and Delta=|{:(,-x,a,b),(,b,-x,a),(,a,b,-x):}|, then

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  8. The determination Delta=|{:(,b,c,balpha+c),(,c,d,calpha+d),(,balpha+c,...

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  9. The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,a...

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  10. If a non-singular matrix and A^(T) denotes the tranpose of A, then

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  11. Let "Let"(x)=|{:(,2sinx,sin^(2)x,0),(,1,2sin x,sin^(2)x),(,0,1,2sin x)...

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  12. Let Delta=|{:(,1,x,x^(2)),(,x^(2),1,x),(,x,x^(2),1):}|,then

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  13. Let f(x)=|{:(,1//x,logx,x^(n)),(,1,-1//n,(-1)^(n)),(,1,a,a^(2)):}| whe...

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  14. If D is determinant of order three of Delta is a determinant formed by...

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  15. Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB a...

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  16. Let A and B be two 2 xx 2 matrix with real entries, If AB=0 and such t...

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  17. If A^(-1)=[{:(,1,-1,0),(,0,-2,1),(,0,0,-1):}] then

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