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For the matrix A=[(2,3),(1,2)] show that...

For the matrix `A=[(2,3),(1,2)]` show that `A^2-4A+I=0` Hence find `A^-1`

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If A=[(5,3),(12,7)] , show that A^(2)-12A-I=0 . Hence find A^(-1) .

If A=[3112], show that A^(2)-5A+7I=0 Hence find A^(-1) .

For the matrix,A=[[1,-12,3]] show that A^(2)-4A+5I=0 and also find A^(-1)

If A=[{:(3,1),(-1,2):}] , show that A^(2)-5A+7I=O . Hence, find A^(-1) .

If A=[[2,-33,4]], show the A^(2)-6A+17I=0. Hence find A^(-1)

If A=[(2,-1,1),(-1,2,-1),(1,-1,2)] show that A^(2)-5A+4I=0 Hence find A^(-1)

If A= [[3,1] , [-1,2]] then show that A^2 - 5A+7I =0 Hence find A^(-1)

For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0 . Hence find A^(-1)

If A=[(4,2),(-1,1)] , show that (A-2 I) A-3 I) =0

For the matrix A=[[3,17,5]], find x and y sot that A^(2)+xI+yA=0 Hence,Find A^(-1)

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Solve the following differential equation : (1+"y"^2)(1+log"x")"dx"+"...

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  2. Using the properties of determinants, prove the following |(1,bc,bc(b+...

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  3. For the matrix A=[(2,3),(1,2)] show that A^2-4A+I=0 Hence find A^-1

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  4. Form the differential equation of the family of curves "y"="A e"^("...

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  5. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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  6. An urn contains 6 red and 5 blue balls. Two balls are drawn at rand...

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  7. A particle is projected with a velocity of 39.2 m/sec at an elevati...

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  8. Find the resultant of two velocities 6 km/hr and 6\ sqrt(2) km/hr i...

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  9. Two forces act at a point and are such that if the direction of one...

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  10. Find the equation of the plane passing through the intersection of ...

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  11. Find the equation of the sphere which passing through the points (0...

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  12. Find the value of lambda , which makes the vectors vec a ,\ vec b...

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  13. A particle starting with initial velocity of 26 m/sec moves with a ...

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  14. A body of mass 50 kg, suspended by two strings of lengths 30 cm and...

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  15. Find the point on the curve y^2=4x which is nearest to the point (2, 1...

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  16. Show that a cylinder of a given volume which is open at the top has...

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  17. If y=acos(logx)+sin(logx), prove that (x^2d^2)/(dx^2)+\ x(dy)/(dx)+y=...

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  18. Verify Rolle's theorem for the function on f(x)=\ x^2-5x+6 on [2, 3].

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  19. Using matrices, solve the following system of equations: 2x-y+z=\ -3,...

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  20. Evaluate : int(2x-3)/(x^2+\ 3x-18)\ dx

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