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We define a binary relation ~ on the set...

We define a binary relation ~ on the set of all `3xx3` real matrices as A~B if and only if there exist invertible matrices P and Q such that `B = PAQ^-1`. The binary realtion is

A

1) neither reflexive nor symmetric

B

2) reflexive, and symmetric but not transitive

C

3) symmetric and transitive but not reflexive

D

4) all equivalence relation.

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MODERN PUBLICATION-MATRICES-EXERCISE
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  3. We define a binary relation ~ on the set of all 3xx3 real matrices as ...

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  4. If A is a 3xx4 matrix and B is a matrix such that A'B and BA' are both...

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  5. If {:[(e^x,e^y),(e^y, e^x)]=[(1,1),(1,1)], then the values of x and y ...

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  6. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

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  7. The number of 3xx3 matrices A whose are ether 0 or 1 and for which t...

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  8. If omegane1 is the complex cube root of unity and matix H = {:[(omega,...

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  9. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

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  10. If A=[[1,2,2],[2,1,-2],[a,2,b]] is a matrix satisfying the equation ...

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  11. If A = [[5a, -b],[3,2]] and a "dj" A = A A^(T), then 5a+b is equal to

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  12. Let P = {:[(1,0,0),(4,1,0),(16,4,1)] and I be te identity matrix of or...

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  13. Write the element a12 of the matrix A = [a(ij)](2xx2) a(ij) = e^(2ix...

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  14. If A=[(3,-3),(-3,3)] and A^2=lambdaA then find lambda.

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  15. For what value of 'x', is the matrix: A = {:[(0,1,-2),(-1,0,3),(x,-3...

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  16. If {:2[(3,4),(5,x)] + [(1,y ),(0,1)] = [(7,0),(10,5)], find (x-y).

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  17. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

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  18. Show that A + A' is symmetric when A = {:[(2,4),(5,6)].

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  19. By using elementary transformation, find the inverse of the matrix ...

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  20. If A= ((-1,-4),(1,3)), then prove by Mathematical Induction that : A^n...

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