to the right of the equal sign, you have the given values p0, p1, p2,... up to pn, and components of vector p, and i must now write the coefficients of the matrix t,  ta equals p, where the first line is and secondly we have another method that will give us an explicit formula for the polynomial p(t). and so on up to p(tn) which must equal pn. and then i have n+1 equations where p(t0)  has to equal p0, the first equation and we will now talk about lagrangian interpolation. in order to know the coefficients. p(t)= a0 + a1t + a2t²+ ... +  up to an*(t to the power of n). similarly p(t1) should equal p1 and this is equal to since the unknows a0, a1, a2 interact in a linear manner. so a0 + a1 times t0 + a2 times t0 squared + ... + an times (t0 to the power of n) should be equal to p0; there is a large number of operations  required to solve a linear system. these are the coefficients of the of the polynominial in the canonic base: