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State True/False: Every rectangular matrix can be expressed as sum of symmetric and skew symmetric matrices.

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JMD PUBLICATION-MATRICES-EXERCISE
  1. If A = [[0,a,3],[2,b+2,-1],[-3,1,0]] is skew symmetric, then 2a + b =

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  2. If A,B are symmetric matrices of the same order,then AB - BA is

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  3. Matrices A and B will be inverse of each other if

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  4. If A = [1,2,3] and B = [[2],[4],[6]],then AB is

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  5. State True/False: If A is a symmetric matrix ,then A' = -A

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  6. State True/False: Every rectangular matrix can be expressed as sum of ...

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  7. State True/False: If A is of order 2 × 3 and B is of order 3 × 4,then ...

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  8. If (A =[[2,3],[4,5]]), prove that A-A' is a skew symmetric matrix wher...

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  9. IF(A=[[3,-4],[-1,2]]), find a matrix B such thet (AB = 1)

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  10. Construct a (2 times 2) matrix where (a(ij)=(i+(2)j)^(2)/(4))

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  11. If (A=[[3,-2],[4,-2]]), find K such that (A^2=KA - 2I2).

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  12. Find x and y, if (2[[1,3],[0,x]]+[[y,0],[1,2]]=[[5,6],[1,8]])

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  13. Show that the matrix BAB) is symmetric or skew symmetric according as ...

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  14. For the matrix (A=[[-3,6,0],[4,-5,8],[0,-7,-2]]), find (1/2(A-A')), wh...

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  15. Construct a (2 times 2) matrix where (a(ij)=(3i-j)/2).

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  16. If A=[[i,0],[0,-i]] and B=[[0,i],[i,0]], show that AB !=BA.

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  17. Solve for x and y, ([[3,-4],[1,2]][[x],[y]]=[[3],[11]])

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  18. If ([[ cosx,sinx],[-sinx,cosx]]), find x, (0<x<pi/2) when (A + A' = 1)...

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  19. (1+costheta+sintheta)/(1+costheta-sintheta)=(1+sintheta)/costheta .

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  20. Write the element (a23) of (a 3 times 3) matrix (A = (aij)), whose ele...

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