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Construct the matrix A = [a(ij)](3xx3), ...

Construct the matrix A = `[a_(ij)]_(3xx3),` where `a_(ij)=i-j`. State whether A is symmetric or skew- symmetric.

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The correct Answer is:
Skew symmetric
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PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-SOLUTION TO EXERCISE 7.1
  1. Given your own examples of matrices satisfying the conditions in each ...

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  2. Show that f (x) f (y) = f(x+y) , where f(x)=[(cosx,-sinx,0),(sinx,co...

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  3. If A is a square matrix such that A^(2) = A, find the value of 7A-(I+A...

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  4. Verify the property A(B+C) = AB+AC, when the matrices A,B, and C are g...

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  5. Find the matrix A which satisfies the matrix relation A [(1,2,3),(4,5,...

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  6. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

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  7. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

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  8. If A^(T)=[(4,5),(-1,0),(2,3)]and B=[(2,-1,1),(7,5,-2)], verify the ...

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  9. If A is a 3xx4 matrix and B is a matrix such that both A^(T)B and BA^(...

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  10. Express the matrices as the sum of a symmetric matrix and a skew -sym...

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  11. Express the matrices as the sum of a symmetric matrix and a skew -symm...

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  12. Find the matrix A such that [(2,-1),(1,0),(-3,4)]A=[(-1,-8,10),(1,2,-5...

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  13. If A=[(1,2,2),(2,1,-2),(x,2,y)] is a matrix such that "AA"^(T) =9I, fi...

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  14. For what value of x, the matrix A=[(0,1,-2),(-1,0,x^(3)),(2,-3,0)] is ...

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  15. If [(0,p,3),(2,q^(2),-1),(r,1,0)] is skew- symmetric, find the values ...

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  16. Construct the matrix A = [a(ij)](3xx3), where a(ij)=i-j. State whether...

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  17. Let A and B be two symmetric matrices. Prove that AB= BA if and only i...

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  18. If A and B are symmetric matrices of same order, prove that AB+BA is...

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  19. If A and B are symmetric matrices of same order, prove that AB-BA is...

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  20. A shopkeeper in a Nuts and Spices shop makes gift packs of cashew Nuts...

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