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If A=[-1 1 0-2] , then prove that A^2+3A...

If `A=[-1 1 0-2]` , then prove that `A^2+3A+2I=Odot` Hence, find `Ba n dC` matrices of order 2 with integer elements, if `A=B^3+C^3dot`

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To solve the problem, we will follow these steps: ### Step 1: Define the Matrix A Given the matrix \( A \): \[ A = \begin{pmatrix} -1 & 1 \\ 0 & -2 \end{pmatrix} \] ...
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CENGAGE ENGLISH-MATRICES-ILLUSTRATION
  1. Let A, B, C, D be (not necessarily square) real matrices such that A^T...

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  2. If A and B are square matrices of the same order such that A B = B A,...

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  3. If A=[-1 1 0-2] , then prove that A^2+3A+2I=Odot Hence, find Ba n dC m...

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  4. If A=[(3,-4),(1,-1)] then find tr. (A^(2012)).

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  5. If A is a nonsingular matrix satisfying AB-BA=A, then prove that det. ...

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  6. If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B and B^(3)A=A^(3)B, the...

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  7. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

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  8. If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an iden...

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  9. Consider point P(x, y) in first quadrant. Its reflection about x-axis ...

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  10. If A=[[2,-2,-4],[-1,3,4],[1,-2,-3]] then A is 1) an idempotent matrix ...

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  11. If A= [(1,1,3),(5,2,6),(-2,-1,-3)] then find A^(14)+3A-2I

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  12. The matrix A=[-5-8 0 3 5 0 1 2-] is a. idempotent matrix b. involut...

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  13. If abc=p and A=[(a,b,c),(c,a,b),(b,c,a)], prove that A is orthogonal i...

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  14. Let A be an orthogonal matrix, and B is a matrix such that AB=BA, then...

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  15. Find the adjoint of the matrix A=[(1,1,1),(2,1,-3),(-1,2,3)].

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  16. If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(...

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  17. If A is a square matrix such that A(adjA)=[(4,0,0),(0,4,0),(0,0,4)], t...

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  18. Let A be a square matrix of order 3 such that adj. (adj. (adj. A)) =...

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  19. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

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  20. Matrices a and B satisfy AB=B^(-1), where B=[(2,-1),(2,0)]. Find (i...

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