Question

Please help me write a MATLAB program that constructs a column matrix b, such that

b₁ = 3x₁ – 3/4y₀
b₂ = 3x₂
…
b_n-2 = 3x_n-2
b_n-1 = 3x_n-1 – 3/4y_n

where x and y are variables. Notice that y only appears in the first and last entries of b.

My problem is that I don’t know how variables work in MATLAB. I tried

b = 3*x

and it says

??? Undefined function or variable ‘x’

So, how do we create variables instead of constants?

Thanks!

Answer 1

EDIT:

From your comments above, what you need is MATLAB’s symbolic toolbox, which allows you to perform computations in terms of variables (without assigning an explicit value to them). Here’s a small example:

syms x %#declare x to be a symbolic variable
y=1+x;
z=expand(y^2)

z=
 
x^2 + 2*x + 1

You will need to use expand sometimes to get the full form of the polynomial, because the default behaviour is to keep it in its simplest form, which is (1+x)^2. Here’s another example to find the roots of a general quadratic

syms a b c x
y=a*x^2+b*x+c;
solve(y)

ans =
 
 -(b + (b^2 - 4*a*c)^(1/2))/(2*a)
 -(b - (b^2 - 4*a*c)^(1/2))/(2*a)

---

I think you meant bn and xn in the last line… Anyway, here’s how you do it:

b=3*x;
b([1,end])=b([1,end])-3/4*y([1,end])

You can also do it in a single line as

b=3*x-3/4*[y(1); zeros(n-2,1); y(end)];

where n is the length of your vector.