Book about interpolation of functions by polynomials using linear algebra/projection

Question

I've been asking a lot of questions about interpolation of functions using polynomials:

Approximate $f(t) = 1-|2t-5|$ in $[2,3]$ by $p\in P_2$ by using the least squares method

Approximate $f(x) = x^{1/3}$ by $p(x)$ of degree $\le 2$ that minimizes the error $E = (f(-1)-p(-1))^2 + \int_{-1}^1 (f(x)-p(x))^2 dx + (f(1)-p(1))^2$

Fitting points to curve $g(t) = \frac{100}{1+\alpha e^{-\beta t}}$ by thinking about projections and inner products

Find polynomial of smallest norm and of degree $\le 3$ for which $p(0) = 2$

And all the answer i've been receiving are based on calculus\, taking derivatives. However, I'm studying linear algebra numerical methods in the context of projections onto polynomial spaces and using orthogonal families of polynomials.

Do anyone know a book that treats interpolation, smallest norm finding and other related things in a linear algebra way?