<s>[INST] How to symbolically solve a system of linear equations A fellow user had an interesting question:

Less-tedious way of solving this system of linear equations?
Is there a shortcut to solving for $w_1, w_2, w_3$ in $$
  \left[ \begin{array}{ccc}  1 & 1 & 1\\  \frac{3}{4}a+\frac{1}{4}b &
 \frac{1}{2}a+\frac{1}{2}b & \frac{1}{4}a+\frac{3}{4}b\\
  (\frac{3}{4}a+\frac{1}{4}b)^2 & (\frac{1}{2}a+\frac{1}{2}b)^2 &
 (\frac{1}{4}a+\frac{3}{4}b)^2\\  \end{array} \right]  \cdot
  \left[ \begin{array}{c}  w_1\\  w_2\\  w_3  \end{array} \right]  =
  \left[ \begin{array}{c}  b-a\\  \frac{b^2-a^2}{2}\\
  \frac{b^3-a^3}{3}  \end{array} \right]   $$ where $a, b$ are
  constants? (I'm trying to derive the formula for a 3-point open
  Newton-Cotes quadrature rule.) Thanks!

Unfortunately the question was deleted (link), but I think it might be interesting in general.
 [/INST] One way is to use the free Maxima computer algebra system.
You can enter your matrix like this:</s>