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 = { }
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 = { }
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.