Solved

# linear algebra

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.

-lj8866