I answered a test question incorrectly and now studying for finals i need to know if this is the correct way to work the problem...
Consider two bases of P2, E: x-2x^2, 1-3x, x^2 and F: 1, 1+x, 1+x+x^2
a. If the polynomial f(x) has the coordinate matrix (1,2,3) with respect to the basis E, what is the coordinate matrix of f with respect to basis F?
b. What is this polynomial f(x)?
I iniatially had the matrix set up like this
[ 1 1 1 | 1 0 0]
[ 0 1 1 | 0 -3 1]
[ 0 0 1 | -2 1 0]
Note: In the middle that is just to clearly seperate the 3x3's into F and E ( F | E) --> ( I | P)
But the right half was underlined.. so im assuming that the left is correct. I also am thinking that the matrix may be written like this instead?
[ 1 1 1 | 0 1 0]
[ 0 1 1 | 1 -3 0]
[ 0 0 1 | -2 1 0]
I am not worried about solving it to get the I on the left side just yet, just setting up the problem.
thanks in advance.
Consider two bases of P2, E: x-2x^2, 1-3x, x^2 and F: 1, 1+x, 1+x+x^2
a. If the polynomial f(x) has the coordinate matrix (1,2,3) with respect to the basis E, what is the coordinate matrix of f with respect to basis F?
b. What is this polynomial f(x)?
I iniatially had the matrix set up like this
[ 1 1 1 | 1 0 0]
[ 0 1 1 | 0 -3 1]
[ 0 0 1 | -2 1 0]
Note: In the middle that is just to clearly seperate the 3x3's into F and E ( F | E) --> ( I | P)
But the right half was underlined.. so im assuming that the left is correct. I also am thinking that the matrix may be written like this instead?
[ 1 1 1 | 0 1 0]
[ 0 1 1 | 1 -3 0]
[ 0 0 1 | -2 1 0]
I am not worried about solving it to get the I on the left side just yet, just setting up the problem.
thanks in advance.