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For any n xx n matrix A, prove that A ca...

For any `n xx n` matrix A, prove that A can be uniquely expressed as a sum of a symmetric matrix and a skew symmetric matrix.

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The correct Answer is:
`C=1/2 (A-A')`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -SOLVED PROBLEMS
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  2. If [(0,4,-2),(-4,0,8),(2,-8,x)] is a skew symmetric matrix then find t...

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  3. For any n xx n matrix A, prove that A can be uniquely expressed as a s...

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  4. Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

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  5. Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),...

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  6. Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(a...

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  7. find determinant of |(1, omega, omega^(2)),(omega, omega^(2),1),(omega...

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  8. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  9. Show that the determinant of skew - symmetric matrix of order three is...

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  10. Fiind the valueof x if: |{:(x-2, 2x-3, 3x-4),(x-4, 2x-9, 3x-16),(x-8...

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  11. Find the Adjoint and Inverse of the matrix A = [(1,2),(3,-5)]

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  12. Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1...

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  13. Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular a...

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  14. Find the rank of A=[{:(0,1,2),(1,2,3),(3,2,1):}] using elementary tran...

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  15. Find the rank of A=[{:(1,2,0,-1),(3,4,1,2),(-2,3,2,5):}] using element...

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  16. Apply the test of rank to examine whether the following equations are ...

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  17. Solve the following system of equations by using Cramer,s ruel . 3x...

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  18. Solve the equations 3x+4y+5z=18,2x+y+8z=13,5x-2y+7z=20 by matrix inver...

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  19. Solve the following system of equations by using Cramer,s ruel . 3x...

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  20. Solve the system of equations 2x+4y-z=0,x+2y+2z=5,3x+6y-7z=2 by Gauss ...

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