enote each of the 4 vectors vi = [fi(x)]b to be the coordinate vector of fi(x) relative to the basis b = {1, x, x2, x3, x4} in p4. define these as column vectors in matlab as v1, v2, in matlab

To define each vector vi = [fi(x)]b as a coordinate vector relative to the basis b in p4, you can use the following steps in MATLAB:

1. Define the polynomial functions fi(x) as symbolic expressions.
2. Create a cell array b that represents the basis elements {1, x, x^2, x^3, x^4}.
3. Create vectors v1 and v2 as column vectors using the coordinate vector representation.

Here's the MATLAB code to accomplish this:

main.m
syms x
% Define the polynomial functions f1(x) and f2(x) as symbolic expressions
f1 = x^2 + 3*x + 1;
f2 = 2*x^4 - x^2 + 5;

% Create the basis array b
b = {1, x, x^2, x^3, x^4};

% Create the coordinate vectors v1 and v2
v1 = [subs(f1, x, b{1}); subs(f1, x, b{2}); subs(f1, x, b{3}); subs(f1, x, b{4}); subs(f1, x, b{5})];
v2 = [subs(f2, x, b{1}); subs(f2, x, b{2}); subs(f2, x, b{3}); subs(f2, x, b{4}); subs(f2, x, b{5})];
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In this code, subs(f, x, b{i}) is used to substitute the basis element b{i} into the polynomial function f. The resulting value is then added to the coordinate vector v1 or v2.

Now, v1 and v2 are column vectors in MATLAB representing the coordinate vectors of f1(x) and f2(x) relative to the basis b in p4.