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For the matrix A=[1 1 1 1 2-3 2-1 3] . S...

For the matrix `A=[1 1 1 1 2-3 2-1 3]` . Show that `A^3-6A^2+5A+11\ I_3=O` . Hence, find `A^(-1)` .

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Given `A=[(1, 1, 1),( 1, 2,-3),( 2, 1, 3)]`.
`"To prove" A^3-6A^2+5A+11 I=0`
`A^2=[(1, 1, 1),( 1, 2,-3),( 2, 1, 3)][(1, 1, 1),( 1, 2,-3),( 2, 1, 3)]`
`A^2=[[1+1+2 , 1+2-1 , 1-3+3],[1+2-6 , 1+4+3 , 1-6-9],[2-1+6 , 2-2-3 , 2+3+9]]`
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NCERT ENGLISH-DETERMINANTS-All Questions
  1. Find values of k if area of triangle is 4 sq. units and vertices are ...

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  2. For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I3=O ...

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  3. For the matrix A=[[3,2],[1,1]], find the numbers a and b such that A^2...

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  4. If A=[[1, 1,-2],[ 2, 1,-3],[ 5, 4,-9]]. Find |A|.

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  5. Find values of x, if(i) |(2, 4),( 5, 1)|-|(2x,4),( 6,x)| (ii) |(2, 3)...

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  6. If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]], then show that |3A| = 27|A|

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  7. Evaluate the determinants (i) |(3,-1,-2),( 0, 0,-1),( 3,-5, 0)| (ii) ...

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  8. Evaluate the determinants in(i) |(costheta,-sintheta),(sintheta,costhe...

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  9. If A=[[1,2],[4,2]], then show that |2A|=4|A|

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  10. Evaluate the determinants |(2, 4),(-5,-1)|

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  11. If |[x,2],[18 ,x]|=|[6, 2],[ 18, 6]|, then x is equal to (A) 6 (B) pm ...

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  12. Solve system of linear equations, using matrix method, 2x + 3y +3z = ...

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  13. Evaluate |(2, 4),(-1,2)|

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  14. Evaluate |(x, x+1),(x-1,x)|

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  15. Find values of x for which|(3, x),(x,1)| = |(3, 2),(4,1)|

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  16. Evaluate Delta=|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

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  17. Find minors and cofactors of the elements of the determinant|2-3 5 6 ...

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  18. Verify Property 1 for Delta=|(2,-3 ,5),(6, 0 ,4 ),(1,5,-7)|

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  19. Write the value of the following determinant: |[102, 18, 36],[ 1, 3, 4...

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  20. Evaluate Delta=|3 2 3 2 2 3 3 2 3|

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