Find a polynomial in P2 if possible that fits the following

Find a polynomial in P_2, if possible, that fits the following data: (-2, 6), (3, 7) (-2, 6), (3, 7), (4, 7) (-2, 6), (3, 7), (4, 7), (5, 8)

Solution

t² + 1 [ 1 , 0 , 1 ]
t² + t [ 1 , 1 , 0 ]
t + 1 = [ 0 , 1 , 1 ]

Make a matrix:
[ 1 , 0 , 1 ]
[ 1 , 1 , 0 ]
[ 0 , 1 ,1 ]

The determinant is 2, so the rows are linearly independent. Thus they span P2.

we will see that b fits the following when we do by using row echolen