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If A^(3)=O, then prove that (I-A)^(-1) =...

If `A^(3)=O`, then prove that `(I-A)^(-1) =I+A+A^(2)`.

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To prove that if \( A^3 = O \) (where \( O \) is the zero matrix), then \( (I - A)^{-1} = I + A + A^2 \), we will follow these steps: ### Step 1: Start with the expression for the inverse We want to show that: \[ (I - A)(I + A + A^2) = I \] ...
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CENGAGE ENGLISH-MATRICES-CAE 13.5
  1. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

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  2. Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and B=[[-x,14x,7x] , [0,1,0] , [x,...

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  3. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

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  4. For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

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  5. If A^(3)=O, then prove that (I-A)^(-1) =I+A+A^(2).

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  6. If A =[[cos alpha,-sin alpha],[sinalpha, cos alpha]] , B= [[cos 2 beta...

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  7. If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),...

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  8. If A is a 2xx2 matrix such that A^(2)-4A+3I=O, then prove that (A+3I)^...

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  9. For two unimobular complex numbers z(1) and z(2), find [(bar(z)(1),-z(...

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  10. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

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  11. If square matrix a is orthogonal, then prove that its inverse is also ...

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  12. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

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  13. Prove that ("adj. "A)^(-1)=("adj. "A^(-1)).

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  14. Using elementary transformation, find the inverse of the matrix A=[(a,...

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  15. If A and P are the square matrices of the same order and if P be inver...

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  16. Show that the characteristics roots of an idempotent matris are either...

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  17. If alpha is a characteristic root of a nonsin-gular matrix, then prove...

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