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Find the matrix A satisfying the matrix ...

Find the matrix A satisfying the matrix equation :
`[{:(2,1),(3,2):}]*A*[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}]`

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The correct Answer is:
`=[{:(1,1),(1,0):}]`
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KUMAR PRAKASHAN-MATRICES -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Find x, if [1" "x" "1][{:(1,3,2),(2,5,1),(15,3,2):}][{:(1),(2),(x):}]=...

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  2. Show that A=[{:(5,3),(-1,-2):}] satisfies the equation A^(2)=3A-7I=0 ...

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  3. Find the matrix A satisfying the matrix equation : [{:(2,1),(3,2):}]...

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  4. Find A , if [{:(4),(1),(3):}]A=[{:(-4,8,4),(-1,2,1),(-3,6,3):}]

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  5. If A=[{:(3,-4),(1,1),(2,0):}]andB=[{:(2,1,2),(1,2,4):}],then verify (B...

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  6. If possible , find BA and AB , where A=[{:(2,1,2),(1,2,4):}],B=[{:...

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  7. Show by an example that for AneO,BneO,AB=O.

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  8. Given A=[{:(2,4,0),(3,9,6):}]andB=[{:(1,4),(2,8),(1,3):}]. Is (AB)'=B'...

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  9. Solve for x and y : x[{:(2),(1):}]+y[{:(3),(5):}]+[{:(-8),(-11):}]=...

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  10. If X and Y are 2xx2 matrices , then solve the following matrix equati...

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  11. If A=[3" " 5],B=[7" " 3] , then find a non - zero matrix C such tha...

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  12. Give an example of matrices A,B and C such that AB=AC, where A is nonz...

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  13. If A=[{:(1,2),(-2,1):}],B=[{:(2,3),(3,-4):}]andC=[{:(1,0),(-1,0):}] ve...

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  14. If P=[{:(x,0,0),(0,y,0),(0,0,z):}]andQ=[{:(a,0,0),(0,b,0),(0,0,c):}], ...

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  15. If [[2" "1" "3][{:(-1,0,-1),(-1,1,0),(0,0,1):}]*[{:(1),(0),(-1):}]=A f...

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  16. If A=[2" "1],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}], veri...

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  17. If A=[{:(1,0,-1),(2,1,3),(0,1,1):}] , then verify that A^(2)+A=A(A+I)...

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  18. If A=[{:(0,-1,2),(4,3,-4):}]andB=[{:(4,0),(1,3),(2,6):}] then verify ...

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  19. If A=[{:(1,2),(4,1),(5,6):}],B=[{:(1,2),(6,4),(7,3):}], then verify th...

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  20. Show that A'A and A A ' are both symmetric matrices for any matrix A .

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