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If A is any matrix, then: (A^(T))^(T) =A...

If A is any matrix, then: `(A^(T))^(T) =A`

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Assertion (A) : The matrix [(cosalpha,sinalpha),(-sinalpha,cosalpha)] is an orthogonal matrix. Reason (R) : If A is an orthogonal matrix then A A^(T)=A^(T)A=I

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If a is a square matrix, then adjA^(T)-(adjA)^(T)=

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If A is a square matrix then show that A+A^(T) and A A^(T) are symmetric and A-A^(T) is skew - symmetric.

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -SOLVED PROBLEMS
  1. Fiind the valueof x if: |{:(x-2, 2x-3, 3x-4),(x-4, 2x-9, 3x-16),(x-8...

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

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

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

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

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

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

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

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

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

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

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  12. Solve the following- system of equations, 2x + 5y + 6z = 0, x - 3y + 8...

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  13. The number of nontrivial solutions of the system: x-y+z=0, x+2y=0, 2x+...

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  14. Theorem: Matrix multiplication is associative, i.e., if conformability...

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  15. Theorem : Matrix multiplication, is distri-butive over matrix addition...

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  16. If A is any matrix, then: (A^(T))^(T) =A

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  17. If A-and B are two matrices of same type, then (A+B)^(T) =A^(T) + B^(T...

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  18. If A and B are two matrices for which conformability for multiplicatio...

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  19. If A is an invertible matrix and A is also invertible then prove (A^(...

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  20. A certain book shop has 10 dozen chemistry books, 8 dozen physics book...

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