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If alphaandbeta are scalars and A is a s...

If `alphaandbeta` are scalars and A is a square matrix then prove that
`(A-alphaI).(A-betaI)=A^(2)-(alpha+beta)A+alphabetaI` where I is a unit matrix of same order as A.

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`=RHS`
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ARIHANT PUBLICATION-MATRICES -ODISHA BUREAU .S TEXTBOOK SOLUTIONS (Exercise (a) )
  1. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  2. If A=[{:(1,2,3),(3,-2,1),(4,2,1):}] , show that A^(3)-23A-40I=0

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  3. Simplify: "[x y z]"xx[[a,h,g],[h,b,f],[g,f,c]]xx[[x],[y],[z]]

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  4. If A and B are matrices of the same order and AB=BA, Then prove that ...

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  5. If A and B are matrices of the same order and AB=BA, Then prove that ...

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  6. If A and B are matrices of the same order and AB=BA, Then prove that ...

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  7. If alphaandbeta are scalars and A is a square matrix then prove that ...

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  8. If alpha "and" beta, are scalars such that A = alpha B+beta I, where A...

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  9. If A=[[-1,3,5],[1,-3,-5],[-1,3,5]]Show that A^2=A.

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  10. If A=[[0,2,3],[2,1,4]] "and" B=[[7,6,3],[1,4,5]] "find " 2A+3B,2A-3B.

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

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

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

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

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  15. [{:(1,-2),(3,2):}][{:(x,2),(1,y):}]=[{:(-3,4),(-1,4):}], find x and y...

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  16. If A=[{:(1,-2,2),(3,1,-1):}]andB=[{:(2,4),(1,2),(3,-1):}] , then veri...

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  17. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

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  18. If[[x,y],[x,x/2+t]]+[[y,x+t],[x+2,x/2]]=[[1,4],[2,3]] find x,y,z and t...

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  19. There are two families A and B . There are 4 men , 6 women and 2 child...

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  20. A trust fund has Rs. 50,000 that is to be invested in two types of ...

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