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If `A=[(1, 2, 2),( 2, 1, 2), (2, 2, 1)],` verify that `A^2-4A-5I=0`

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If A=[(1, 2 ,2 ),(2 ,1 ,2),( 2 ,2, 1)] , then prove that A^2-4A-5I=O .

If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I) , where I is the identity matrix.

Show that the matrix A=[[1 ,2, 2],[ 2, 1, 2],[ 2, 2, 1]] satisfies the equation A^2-4A-5I_3=O and hence find A^(-1) .

If A=[1 2 2 2 1 2 2 2 1] , find A^(-1) and prove that A^2-4A-5I=O .

If A=[(2, 3),( 1, 2)] , verify that A^2-4A+I=O , where I=[(1, 0),( 0, 1)] and O=[(0, 0),( 0, 0)] . Hence, find A^(-1) .

If A=[{:(1,0,-1),(2,1,3),(0,1, 1):}] then verify that A^(2)+A=A(A+I) , where I is 3xx3 unit matrix.

If A=[1 2 2 2 1 2 2 2 1] , then show that A^2-4A-5I=O ,w h e r eIa n d0 are the unit matrix and the null matrix of order 3, respectively. Use this result to find A^(-1)dot

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=0 and hence find A^(-1)

If A+I={:[(2,2,3),(3,-1,1),(4,2,2)]:} then show that A^(3)-23A-40I=0

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
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  2. Find the angle between the vectors vec a= hat i- hat j+\ hat k\ a...

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  3. If A=[(1, 2, 2),( 2, 1, 2), (2, 2, 1)], verify that A^2-4A-5I=0

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  5. Using properties of determinants, prove the following: \begin{vmatr...

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  7. Find the value of sin[pi/3 - sin^(-1) (- 1/2)]

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  8. Find the value of x\ and y\ if "2" [(1,3) ,(0,x)]+ "[(y ,0 ),(1 ,2)]...

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  10. Find the cofactor of a(12) in the following: [(2,-3,5), (6 ,0 ,4), (...

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  11. Evaluate int(x^2)/(1+x^3)\ dx"

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  12. Evaluate : int0^1(dx)/(1+x^2)

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  13. A factory owner purchases two types of machines, A and B for his fac...

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  14. An insurance company insured 2000 scooter drivers, 4000 car drivers...

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  15. Evaluate: int(-a)^a\ sqrt((a-x)/(a+x))\ dx\ \

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  16. Find the equation of the plane passing through the point (3,4,1) an...

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  17. Find the shortest distance between the following lines: (x-3)/1=(y-5)/...

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  18. Find the point on the line (x+2)/3=(y+1\ )/2=(z-3\ )/2 at a distanc...

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  19. Evaluate : intsec^2(7-4x)dx

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  20. Write the adjoint of the following matrix: [[2,-1],[4,3]]

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