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If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then ...

If `A=[{:(1,2,1),(2,1,3),(1,1,0):}]` then prove that `A^3-2A^2-7A-4I_3=0`. Hence find `A^(-1)`

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The correct Answer is:
`A^(-1)=1/4[{:(-3,1,5),(3,1,-1),(1,1,5):}]`
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KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. If A=[{:(3,1),(7,5):}] and A^2+xI=yA then find X and Y. Hence find A^(...

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

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  3. If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I3=0. ...

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  4. If A=[{:(2,3),(1,-4):}],B=[{:(1,-20),(-1,3):}] then verify (AB)^(-1)=B...

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  5. A=[{:(2,-3),(4,6):}] verify (adjA)^(-1)=(adjA^(-1))

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  6. Solve system of linear equations , using matrix method if exists 3x+...

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  7. Solve system of linear equations , using matrix method if exists 3x-...

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  8. Solve system of linear equations , using matrix method if exists 5x-...

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  9. Solve system of linear equations , using matrix method if exists 5x+...

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  10. Solve system of linear equations , using matrix method if exists x-y...

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  11. Solve system of linear equations , using matrix method if exists 3x+...

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  12. Solve system of linear equations , using matrix method if exists 2/x...

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  13. Solve system of linear equations , using matrix method if exists x-2...

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  14. Solve system of linear equations , using matrix method if exists 4x-...

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  15. Solve system of linear equations , using matrix method if exists x-y...

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  16. The sum of three numbrs is 6. If we multiply third number by 3 and add...

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  17. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

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  18. If anebnecand |{:(a,a^3,a^4-1),(b,b^3,b^4-1),(c,c^3,c^4-1):}|=0 then p...

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  19. Prove that |{:(sqrt(13)+sqrt3,2sqrt5,sqrt5),(sqrt(15)+sqrt(26),5,sqrt(...

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  20. Prove that |{:(x^2,y^2,z^2),((x+1)^2,(y+1)^2,(z+1)^2),((x-1)^2,(y-1)^2...

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