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Verify that A=[[a,b],[c,d]] satisfies ...

Verify that `A=[[a,b],[c,d]]`
satisfies the equation `A^2-(a+d)A+(ad-bc) I=0` where `I` is the `2`x`2` unit matrix.

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MBD PUBLICATION-MATRICES-QUESTION BANK
  1. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  2. Verify that [AB]^T = B^T A^T whereA=[[1,2],[2,3],[3,4]]=[[2,3,0],[1,2,...

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  3. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  4. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

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

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

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

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

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

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

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  12. 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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  13. If A=[[1,0,-2],[2,3,-1]], B=[[4,-1,3],[0,2,1]]"and" C=[[2,-3,0],[1,4,...

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  14. If A=[[1,0,-2],[2,3,-1]], B=[[4,-1,3],[0,2,1]]"and" C=[[2,-3,0],[1,4,...

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  15. If A=[[1,0,-2],[2,3,-1]], B=[[4,-1,3],[0,2,1]]"and" C=[[2,-3,0],[1,4,5...

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  16. If A=[[2,1],[-1,3]], B=[[2,3],[1,1]] "and" C=[[1,0,2],[-2,3,0]],verify...

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  17. [[1,-2],[3,2]][[x,2],[1,y]]=[[-3,4],[-1,4]]Find x and y.

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  18. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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

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  20. 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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