Hi,
Would you help me with this, please!
Let V be the vector space over the reals R consisting of the polynomials in x of degree at most 4 with coefficients in R, and with the usual addition of vectors (i.e., polinomials) and scalar multiplication.
Let B1={1,x,x^2,x^3,x^4} be the standard ordered basis of V. Let W be the vector space of 2x3 matrices over R with the usual addition of matrices and scalar multiplication. Let B2 be the ordered basis of W given as follows: B2={v1=|1 0 0|;v2=|0 1 0|;v3=|0 0 1|;v4=|0 0 0|;v5=|0 0 0|;v6=|0 0 0|}.
__________________________|0 0 0| |0 0 0| |0 0 0| |1 0 0| |0 1 0| |0 0 1|
Define T: -> W by:
For f=a0+a1x+a2x^2+a3x^3+a4x^4, put
T(f)=( 0 a3 a2+a4
_____a1+a0 a0 0 )
Construct the matrix A=[T]_B1,B2 that represent T with respecr to the pair B1, B2 of ordered bases.
Thank you so much!