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Verify that [AB]^T = B^T A^T whereA=[[1,...

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

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Verify that [AB]^T = B^T A^T where A=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],[-1,1]]

Verify that [AB]^T =B^TA^T where A=[[1,2,3],[6,7,8],[6,-3,4]] B=[[1,2,3],[3,4,2],[5,6,1]] .

Verify that (AB)^(T) = B^(T)A^(T) where A=|[1,-2,2],[3,1,-1]| and B=|[2,4],[1,2],[3,-2]| .

Verify that (AB)^-1=B^-1A^-1 if A=[[1,2,3,],[4,5,6,],[7,8,9,]],B=[[1,2,0,],[2,3,-1,],[1,-1,3,]]

Verify that (AB)^-1=B^-1A^-1 if A=[[2,3,],[1,-1,]],B=[[0,1,],[3,1,]]

If A= [[1,2],[-2,3]]B=[[3,2],[1,4]],C=[[2,2],[1,3]] Calculate AB.

Determine the matrices A and B where A+2B=[[1,2,0],[6,-3,3],[-5,3,1]] and 2A-B=[[2,-1,5],[2,-1,6],[0,1,2]] .

If A= [[1,2,0],[0,1,3],[-2,5,3]],"then verify that" A=[[1,2,0],[0,1,3],[-2,5,3]] impliesA'=[[1,0,-2],[2,1,5],[0,3,3]] A+A' is symmetric

If A= [[1,2,0],[0,1,3],[-2,5,3]],"then verify that" A=[[1,2,0],[0,1,3],[-2,5,3]] impliesA'=[[1,0,-2],[2,1,5],[0,3,3]] A+A' is skmmetric

For the matrices A and B , verify that (AB) =B'A' , where A=[{:(1,),(-4,),(3,):}]andB=[{:(-1,2,1):}] .

MODERN PUBLICATION-MATRICES-PROBLEM
  1. What is A+B if A=((1,2),(3,-1)) B=((0,-1),(-2,1)) ?

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  2. Give an example of a unit matrix.

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  3. Express A=((1,2),(2,3) as the sum of a symmetric and a skew symmetric ...

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  4. If ((x(1),x(2)),((y(1),y(2))-((2,3),(0,1)),=((3,5),(1,2)) then find x(...

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  5. Construct a 2 x 3 matrix having elements defined by a(ij)=i-j.

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  6. Find x,y if A=A^’ where A=((5,x),(y,0))

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  7. If A=((3,0,0),(0.3,0)(0,0,3) then find A^2.

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  8. Can a matrix be constructed by taking 29 elements?

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

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  10. There are two families A and B. There are 4 men, 6 women and 2 childre...

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

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  12. Prove that a unit matrix is its own inverse. Is the converse true ?

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  13. Express as a sum of a symmetric and skew symmetric matrix. [(2,-1,3),(...

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  14. Express as a sum of a symmetric and skew symmetric matrix. [(x,a,b),(a...

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  15. Show that A =((2,-3)(3,4)) satisfies equation x^2-6x+17=0. Hence find ...

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  16. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  17. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

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  18. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

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