Posted on 2003-03-24
I have two questions, but what would help more is if someone explained the concepts behind the problems.
y1 = [1,1,1]T
y2 = [1,1,0]T
y3 = [1,0,0]T
and I is the identity operator on R^3
Find coordinates of I(e1), I(e2), I(e3) with respect to [y1,y2,y3]
and find a matrix A such that Ax is the coordinate vector of x with respect to [y1,y2,y3].
If L(c1y1 + c2y2 + c3y3) = (c1 + c2 + c3)y1 + (2c1 + c3)y2 - (2c2 + c3)y3 find a matrix representing L with respect to basis [y1,y2,y3]
and write x as a linear combination of y1, y2, y3 and use the matrix determined above to determine L(x).
x = [7,5,2]T
The second problem is L is the linear operator mapping P2 into R^2 defined by
L(p(x)) = [integral from 0 to 1 of p(x) dx, p(0) ] T
Find a matrix A such that L(alpha + beta * x) = A[alpha, beta]T.
I already have the solutions to these, but I do not understand how they were attained. Could someone explain the process behind how to solve these problems? That would be most helpful. Thank you.