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

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

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`=[-1 " "2 " " 1]`
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Compute the indicated products : (1) [{:(3,-1,4),(2,3,1):}][{:(1,3,4),(2,1,0),(-3,2,3):}] (2) [{:(1,3),(2,1):}][{:(4),(-1):}] (3) [{:(1,4,2),(5,-2,3):}][{:(2,-4),(1,-3),(4,0):}] (4) [1" "2," "3][{:(2),(4),(6):}] (5) [{:(2),(4),(6):}][1" "2," "3]

Show that (i) [{:(5,-1),(6,7):}][{:(2,1),(3,4):}]ne[{:(2,1),(3,4):}][{:(5,-1),(6,7):}] (ii) [{:(1,2,3),(0,1,0),(1,1,0):}][{:(-1,1,0),(0,-1,1),(2,3,4):}]ne[{:(-1,1,0),(0,-1,1),(2,3,4):}][{:(1,2,3),(0,1,0),(1,1,0):}]

If A+B=[{:(4,3,2),(4,1,7),(3,2,0):}]andA-B=[{:(6,1,4),(-4,3,9),(5,8,2):}] Then find A and B.

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

Find the matrix X so that , X[{:(1,2,3),(4,5,6):}]=[{:(-7,-8,-9),(2,4,6):}] .

If [{:(x,0),(1,y):}]-[{:(2,-4),(-3,-4):}]=[{:(3,5),(6,3):}]-[{:(2,1),(2,1):}] then , x=…., y=…..

If A=[{:(8,0),(4,-2),(3,6):}]andB=[{:(2,-2),(4,2),(-5,1):}] , then find the matrix X , such that 2A+3X=5B.

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

Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (ii) [(1),(2),(3)][(2,3,4)] (iii) [(1,-2),(2,3)][(1,2,3),(2,3,1)] (iv) [(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4),(3,0,5)] (v) [(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)] (vi) [(3,-1,3),(-1,0,2)][(2,-3),(1,0),(3,1)]

KUMAR PRAKASHAN-MATRICES -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Show that A=[{:(5,3),(-1,-2):}] satisfies the equation A^(2)=3A-7I=0 ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^...

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