This is a problem of numerical method course $,$

Suppose we have $3$ input datapoints $(1,2),(-2,1),$ and $(3,0)$ with target output for these datapoints

are $10,5,$ and $3$ respectively. Suppose we want to find a linear function that fits the data well in the

least square sense.

a$.$ Write down the linear regression equation for this problem in vector notaiton.

b$.$ Find the expression for MSE for this $($training$)$ data.

c$.$ Write down the normal equation and solve it using Gaussian Elimination.

d$.$ What will be the predicted out for the input $(2,1)?$

Need answers for a$,$b$,$c$,$d $,$ please do mention details of calculation