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If A=[[x, x] , [x, x]] and B=[[x, -x] , ...

If `A=[[x, x] , [x, x]]` and `B=[[x, -x] , [-x, x]]` then prove that `x e^A=1/2(A.e^(2x)+B)` where `e^A= I+A+A^2/(2!)+...`

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FIITJEE-MATHEMATICS TIPS-NUMERICAL DECIMAL BASED QUESTIONS
  1. If A=[[x, x] , [x, x]] and B=[[x, -x] , [-x, x]] then prove that x e^A...

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  2. If in an A.P. a(7)=9 and if a(1)a(2)a(7) is least, then common differ...

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  3. If x, y, z are positive real numbers, then minimum value of (z)/(x+y)+...

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  4. If the difference of the roots of the equation x^(2)-5x+6=0 is same as...

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  5. The minimum value of 'a' for which a^(2)x^(2)+(2a-1)x+1 is non-negativ...

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  6. The minimum value of the expression [3x^(2)+4x+5] (where [.] greatest ...

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  7. Let lambda be real. If. The origin and the complex roots of 2z^(2)+2z+...

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  8. The equation |z-i|+|z+i|=k, k gt 0 can represent an ellipse, if k=

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  9. For |z-1|=1, i tan(("arg"(z-1))/(2))+(2)/(z) is equal to

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  10. The sum of the rational terms in the expansion of (sqrt(2)+ root(5...

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  11. Find out the sum of the coefficients in the expansion of the binomial ...

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  12. A fair coin is tossed 100 times. The probability of getting tails an ...

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  13. The probabilities of two events are 0.25 and 0.50. The total probabili...

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  14. Let A=[{:(x^(2),6,8),(3,y^(2),9),(4,5,z^(2)):}],B=[{:(2x,3,5),(2,2y,6)...

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  15. The number of non-zero diagonal matrices of order 4 satisfying A^(2)=A...

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  16. Find the following system of equations is consistent, (a+1)^3x+(a+2...

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  17. The maximum value of determinant |{:(cos(alpha+beta),sin alpha,-cos al...

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  18. If x+y+z=10, where x,y,z in N. Find the number of solutions of triplet...

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  19. The figures 4, 5, 6, 7, 8 are written in every possible order. The num...

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  20. If a^(2)+b^(2)+c^(2)=1 where, a,b,cin R, then the maximum value of (4a...

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  21. Let vec a , vec b a n d vec c be three vectors having magnitudes 1...

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