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If A = [(1,2,2),(2,1,2),(2,2,1)] then sh...

If `A = [(1,2,2),(2,1,2),(2,2,1)]` then show that `A^(2)-4A-5I = O`.

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AAKASH SERIES-MATRICES -ADDITIONAL EXERCISE
  1. Find the number of 2xx2 matrices that can be formed by using 1,2,3,4 w...

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  2. If a matrix has 13 elements, then find the possible dimensions (orders...

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  3. If A = [(1,2,2),(2,1,2),(2,2,1)] then show that A^(2)-4A-5I = O.

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  4. The order of the matrix A is 3xx5 and that of B is 2xx3. The order of ...

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  5. If [(1,2,3)]B=[(3,4)] then the order of the matrix B is

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  6. A=[(-1,0),(0,2)]impliesA^(3)-A^(2)=

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  7. If A["x y"],B((a,h),(h,b)),C=((x),(y)) then find ABC.

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  8. If A=[(ab,b^(2)),(-a^(2),-ab)] then A is

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  9. If A=((2,-2,-4),(-1,3,4),(1,-2,k)) is an idempotent matrix then find k...

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  10. If A=[(1,1,3),(5,2,6),(-2,-1,-3)] then A is

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  11. If A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] then A is

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  12. If A,B are two idempotent matrices and AB=BA=O then A+B is

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  13. If A is a square matrix then show that A+A^(T) and A A^(T) are symmetr...

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  14. If 5A=[(3,-4),(4,x)] and "AA"^(T)=A^(T)A=I then x=

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  15. If A, B are symmetric matrices of the same order then show that AB-BA ...

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  16. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)], find the conjugate of A.

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  17. If A=[(1,2-3i,3+4i),(2+3i,0,4-5i),(3-4i,4+5i,2)], then show that A is ...

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  18. If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x!=0,y!=0 then D is

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  19. If A=[a(ij)] is a scalar matrix of order nxxn such that a(ij)=k for al...

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  20. If A is a 3xx3 matrix and det(3A)=k(detA) then k=

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