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Prove that every square matrix can be un...

Prove that every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

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FIITJEE-MATRICES -SOLVED PROBLEM
  1. If A,B,C are three matrices such that A=[x, y, z], [(a, h, g),(h, b, f...

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  2. If A=[{:(,1,1,2),(,0,2,1),(,1,0,2):}] show that A^(3)=(5A-I)(A-I)

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  3. Prove that every square matrix can be uniquely expressed as the sum of...

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  4. If B is a real mxn matrix, show that B'B as well as BB'is a symmetric ...

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  5. Solve the following system of equation by matrix method x + y - 2z = 1...

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  6. Solve the following system of equation by matrix method x+2y +3z+1=...

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  7. Find the values of lambda and mu so that the system of equations (i)...

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  8. If A =[{:( 2,5,3),(3,1,2),(1,2,1) :}] then A^(-1) is equal to

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  9. With the help of metrices the solution of the equations 3x+y+2z=3,2x-3...

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  10. If the trace of the matrix A= [{:( x-1 ,0,2,5),( 3, x^(2) - 2 ,4,1),(...

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  11. If A and B are square matrices of order 3, then

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  12. If A and B are any two square matrices of the same order than ,

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  13. IF A = [{:( -2,3,-1),( -1,2,-1),( -6,9,-4) :}] and B = [{:( 1,3,-1),(...

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  14. If A=[{:( 1,-tanx ),( tanx ,1):}] then the value of [A^(T) A^(-1) ] ...

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  15. If A = [{:( alpha , 2),( 2,alpha ) :}] and |A^(3) | = 125 then the val...

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  16. A= [{:( 1,0,0) ,( 0,1,1) , ( 0,-2,4) :}] ,I= [{:( 1,0,0) ,( 0,1,0),( 0...

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  17. If A is a square matrix of order 5 and 9A^(-1) then [adj (adj AJJ] (...

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  18. The set of natural numbers N is partitioned into arrays of rows and co...

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  19. For what value of x, the matrix [{:( 3-x,2,2),( 2,4-x,1),(-2,-4,-1-x)...

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  20. The adjoint of the matrix A= [{:( 1,2),( 3,-5) :}] is

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