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If A=[(1,0,2),(0,2,1),(2,0,3)] and A^3 -...

If `A=[(1,0,2),(0,2,1),(2,0,3)] and A^3 -6A^2 +7A+kI = O` , find the value of k.

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The correct Answer is:
`k=2`
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NCERT TAMIL-MATRICES AND DETERMINANTS -EXERCISE 7.1
  1. Construct an m xx n matrix A= [a(ij)], where a(ij) a is given by a...

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  2. Construct an m xx n matrix A= [a(ij)], where a(ij) a is given by a...

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  3. Find the values of p, q, r, and s if [(p^2 -1,0,-31-q^3),(7,r+1,9),(...

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  4. Determine the value of x + y if [(2x+y ,4x),(5x-7,4x)]=[(7,7y-13),(y,x...

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  5. Determine the matrices A and B if they satisfy 2A - B +[(6,-6,0),(-4...

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  6. If A = [(1,a),(0,1)] then compute A^4

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  7. Consider the matrix Aa=[(cos alpha, - sin alpha),(sinalpha,cos alpha)]...

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  8. Consider the matrix Aa=[(cos alpha, - sin alpha),(sinalpha,cos alpha)]...

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  9. If A=[(4,2),(-1,x)] and such that (A− 2I )(A− 3I ) = O, find the valu...

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  10. If A=[(1,0,2),(0,2,1),(2,0,3)] and A^3 -6A^2 +7A+kI = O , find the val...

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  11. If A is a square matrix such that A^2 = A, find the value of 7A - (I +...

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  12. Find the matrix A which satisfies the matrix relation A [(1,2,3),(4,5...

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  13. If A is a 3 xx 4 matrix and B is a matrix such that both A^(T) B and ...

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  14. Find the matrix A such that [(2,-1),(1,0),(-3,4)]A^T =[(-1,-8,-10),(1,...

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  15. If A = [(1,2,2),(2,1,-2),(x,2,y)] is a matrix such that "AA"^T = 9I ...

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  16. For what value of x, the matrix A=[(0,1,-2),(-1,0,x^3),(2,-3,0)] is s...

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  17. If [(0,p,3),(2,q^2,1),(r,1,0)] is skew-symmetric, find the values of ...

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  18. Construct the matrix A=[a(ij)](3xx3), where a(ij) =i-j where a(ij) = i...

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  19. A shopkeeper in a Nuts and Spices shop makes gift packs of cashew nuts...

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