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show that the matrix A=[(2,-2,-4),(-1,...

show that the matrix
`A=[(2,-2,-4),(-1,3,4),(1,-2,-3)]` is idempotent.

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`A^(2)=A.A=[(2,-2,-4),(-1,3,4),(1,-2,-3)]xx[(2,-2,-4),(-1,3,4),(1,-2,-3)]`
`=[{:(2.2+(-2).(-1)(-4).1),((-1).2+3.(-1)+4.1),(12+(-2).(-1)+(-3).1),(2.(-2)+(-2).3+(-4).(-2)),((-1).(-2)+3.3+4.(-2)),(1.(-2)+(-2).3+(-3).(-2)),(2.(-4)+(-2).4+(-4).(-3)),((-1).(-4)+3.4.+4.(-3)),(1.(-4)+(-2).4+(-3).(-3)):}`
`[(2,-2,-4),(-1,3,4),(1,-2,-3)]=A`
Hence the matrix A is idempotent.
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ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. show that the matrix A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] is idempotent.

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  2. Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=...

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  3. Evluate int 3x^2 dx

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  4. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

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  5. If A^(2)-A+I=O, then A^(-1) is equal to

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  6. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

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  7. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

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  8. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  9. Let A=[{:(1,2),(3,4):}]and B = [{:(a,0),(0,b):}] where a, b are natura...

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  10. If A and B are square matrices of size nxxn such that A^2-B^2 = (A-B)(...

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  11. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

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  12. Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "...

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  13. Let A be a square matrix all of whose entries are integers. Then wh...

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  14. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

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  15. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  16. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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

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  18. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  19. The number of 3xx3 matrices a whose entries are either 0 or 1 and for ...

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  20. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  21. Let p be an odd prime number and T(P) be the following set of 2xx2 m...

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