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If X is a 2 xx 3 matrix such that |X' X|...

If `X` is a `2 xx 3` matrix such that `|X' X|!=0` and `A = I_2 - X(X' X)^(-1) X',` then `A^2` is equal to

A

A

B

I

C

`A^(-1)`

D

none of these

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A
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MCGROW HILL PUBLICATION-MATRICES-EXERCISE ( LEVEL -1) (Single Correct Answer Type Questions)
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  2. If A , B and C are three square matrices of the same size such that B ...

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  3. If X is a 2 xx 3 matrix such that |X' X|!=0 and A = I2 - X(X' X)^(-1) ...

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  4. The matrix A =((p,-q),(q,p)) is orthogonal if and only if

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  5. The values of lambda for which the matrix A =((lambda ,0 ,lambda),(la...

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  6. The values of a for which the matrix A = ((a,a^(2)-1,-3),(a+1,2,a^(...

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  7. Let A(t)=((1,3,2),(2,5,t),(4,7-t,-6)) then the values (s) of t for whi...

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  8. If A=[(a+ib,c+id),(-c+id,a-ib)] and a^(2)+b^(2)+c^(2)+d^(2)=1, then A^...

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  9. If A=[((1)/(2)(e^(ix)+e^(-ix)),(1)/(2)(e^(ix)-e^(-ix))),((1)/(2)(e^(ix...

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  10. If A= [(ab,b^(2)),(-a^(2),-ab)] then A^(2) is equal

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  11. If A is 2xx2 matrix such that A^(2) =O then tr (A) is

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  12. If A = [(a,b),(c,d)] such that A satisfies the relation A^(2)-(a+d) A=...

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  13. If A =[(3,2),(0,1)] then A^(-3) is

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  14. If A is a skew Hermitian matrix then the main diagonal elements of A a...

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  15. If A =[(1,2,1),(0,1,-1),(3,-1,1)] and AA' =I , then x+y is equal to

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  16. If 3A =[(1,2,2),(2,1,-2),(x,2,y)] and A'A =I then x+y is equal to

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  17. If the system of equations ax +y=3,x+2y=3 , 3x+4y=7 is consistent then...

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  18. If the system of equations x+2y-3z=1,(P+2)z=3,(2P+1)y+z=2 is inconsist...

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  19. The system of linear equations x+y+z=2 2x+y-z=3 3x+2y+kz=4 has a...

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  20. If A=[{:(4,x+2),(2x-3,x+1):}] is a symmetric matrix, then x=?

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