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Verify that the matrix equation A^2 - 4a...

Verify that the matrix equation `A^2 - 4a +3I`=0 is satisfied by the matrix `A = [[2,-1],[-1,2]]`, where `I = [[1,0],[0,1]]` and `0= [[0,0],[0,0]]`,

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UNITED BOOK HOUSE-SET 16-EXERCISE
  1. Prove that, tan^(-1) (4/3) + tan^(-1) (12/5) = pi - tan^(-1)(56/33).

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  2. Without expanding, prove that [[41,1,5],[79,7,9],[29,5,3]]=0

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  3. Verify that the matrix equation A^2 - 4a +3I=0 is satisfied by the mat...

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  4. Evaluate lim(x rarr 0) [e^(px) - e^(-qx])/x

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  5. Find (dy)/(dx), whne y = log(x+sqrt (x^2-a^2))

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  6. Examine whether Rolle's theorem is applicable to the following functio...

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  7. Evaluate:int (x dx)/sqrt(3x^2+1)

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  8. Find the intervals in which the function f(x)= x/(x^2+1) is decreasing...

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  9. Using differentials, find the approximate value of (82)^(1/4).

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  10. If the vectors 3 hati - 2hatj + mhatk and -2 hati + hatj + 4 hatk are ...

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  11. Can the numbers 1/2,-1/sqrt2, -1/2 be the direction cosines of a strai...

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  12. Prove that, if P(A//B)=P(A) then P(A^c//B)=P(A^c).

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  13. If the probability of success in a single trials is 0.05, how many Ber...

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  14. Prove that, |[sin A, cosA, sin(A+theta)],[sinB, cosB, sin(B+theta)],[s...

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  15. If A,B,C be the angles of a triangle, then prove that ,abs((-1,cosC,co...

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  16. Solve:|[a+x,a-x,a-x],[a-x,a+x,a-x],[a-x,a-x,a+x]|=0

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  17. If A = |[1,2,-3],[2,3,2],[3,-3,-4]|, find A^(-1)

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  18. If f(x) = xsqrt (x^2+a^2) +a^2 log(xsqrt(x^2+a^2))then find the value ...

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  19. If y = a cos(logx) + b sin(log x), show that,x^2(d^2y)/(dx^2)+x(dy)/(d...

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  20. Integrate:int(2x^2 - 3x+9)/(x^2+4x-5)dx

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