Compute [T]_B and determine whether B is a basis consisting of eigenvectors of T.

a) V= P_2(R), T(a+bx+cx^2)= (-4a+2b-2c)-(7a+3b+7c)x +(7a+b+5c)x^2,

and a basis B= {x-x^2, -1+X^2, -1-x+x^2}

b)V=M_2x2(R),

=

And the basis B = { }

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- Aug 5th 2008, 07:23 PMJuancd08Computing Linear operator on the basis B.
Compute [T]_B and determine whether B is a basis consisting of eigenvectors of T.

a) V= P_2(R), T(a+bx+cx^2)= (-4a+2b-2c)-(7a+3b+7c)x +(7a+b+5c)x^2,

and a basis B= {x-x^2, -1+X^2, -1-x+x^2}

b)V=M_2x2(R),

=

And the basis B = { } - Aug 8th 2008, 01:50 AMbadgerigar
I am going to call the standard basis for E for no good reason

Where is the matrix that converts from basis E to B. We can get the matrix by using the basis vectors as columns. The matrix is simply the inverse of .

B is a basis consisting of eigenvectors of T iff is diagonal.

go for it.