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Let A=[{:(2,-1),(4,2):}]B=[{:(4,3),(-2,1...

Let `A=[{:(2,-1),(4,2):}]B=[{:(4,3),(-2,1):}]andC=[{:(-2,-3),(-1,2):]]` Find the following (1) 2B+3C,(2)A+(B+C),(3)(2A-3B)-Cand4)(B+C)-2A.

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The correct Answer is:
(1) `[{:(2,-3),(-7,8):}]`
(2) `[{:(4,-1),(1,5):}]`
(3) `[{:(-6,-8),(15,-1):}]`
(4) `[{:(-2,2),(-11,-1):}]`
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If A=[{:(1,1,-1),(2,0,3),(3,-1,2):}],B=[{:(1,3),(0,2),(-1,4):}]andC=[{:(1,2,3,-4),(2,0,-2,1):}] , find A(BC) , (AB)C and show that (AB) C=A(BC),

A=[{:(5,-1),(6,7):}],B=[{:(2,1),(3,4):}]andC=[{:(1,3),(-1,4):}] then verify that (i) (A)=A (ii) (A+B)=A+B (iii) (3A)'=3A (iv) (AB)'=B'A'

If A=[2" "1],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}] , verify A*(B+C)=AB+AC .

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If A=[{:(1,2,-3),(5,0,2),(1,-1,1):}],B=[{:(3,-1,2),(4,2,5),(2,0,3):}]andC=[{:(4,1,2),(0,3,2),(1,-2,3):}] , then compute (A+B) and (B-C).Also , verify that A+(B-C) =(A+B)-C.

KUMAR PRAKASHAN-MATRICES -PRACTICE WORK
  1. Find the value of a,b,cand d. [{:(a,3a-b),(2a+c,3b-d):}]=[{:(3,2),...

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  2. Find the value of a,b,c,x,y and z. [{:(x+3,z+4,2y-7),(4x+6,a-1,0),(...

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  3. Let A=[{:(2,-1),(4,2):}]B=[{:(4,3),(-2,1):}]andC=[{:(-2,-3),(-1,2):]] ...

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  4. Compute the indicated products : (1) [{:(3,-1,4),(2,3,1):}][{:(1,3,...

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  5. If A=[{:(1,-1),(0,2),(2,3):}]andB=[{:(1,0),(-1,7):}] then find AB. Al...

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  6. A=[{:(1,-2,3),(-4,2,5):}]andB=[{:(2,3),(4,5),(2,1):}] then find AB and...

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  7. Compute : [{:(1,-1),(0,2),(2,3):}]([{:(1" "0" "2),(2" "0" "1):}]-[{:(0...

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  8. Find X and Y,if X+Y=[{:(5,2),(0,9):}]andX-Y=[{:(3,6),(0,-1):}].

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

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  10. If Y=[{:(4,3),(2,5):}]and3X-Y=[{:(5,0),(1,1):}] then find X.

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  11. If f(x)=x^(2)-2x then find f(A) where A=[{:(0,1,2),(4,5,0),(0,2,3):}]...

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  12. Solve : [{:(x^(2)),(y^(2)):}]+2[{:(2x),(3y):}]=3[{:(7),(-3):}].

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  13. A=[{:(1,4),(3,2),(2,5):}]andB=[{:(-1,2),(0,5),(3,1):}] then find the ...

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  14. Find A^(2)-5A+6I, if A=[{:(2,0,1),(2,1,3),(1,-1,0):}].

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  15. If A=[{:(1,0),(-1,7):}]andA^(2)=8A+KI then find K.

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  16. Prove that , {[{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,...

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  17. If A=[{:(1,alpha),(0,1):}] then by the principle of mathematical indu...

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  18. If A=[{:(0,1,2),(2,-3,0),(1,-1,0):}]andf(x)=x^(3)+4x^(2)-x, then find ...

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  19. If A=[{:(2,3,-4),(5,1,0),(3,-2,5):}]andI=[{:(1,0,0),(0,1,0),(0,0,1):}]...

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  20. Three friends Ram , Shyam and Rahul went to a shop .Ram purchased 12 d...

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