Integrative Applied Mathematics
Problem Set 8
Due: 2023/06/09 23:59
1. Solve Ax=b by least squares and find 𝑝 = 𝐴𝑥% if
1 0
1
𝐴 = &0 1) , 𝑏 = &1)
1 1
0
Verify that the error b-p is perpendicular to the columns of A
2. Find the matrix P that projects every vector b in R3 onto the line in the direction of a = (2,
1, 3).
3. Find the best straight-line fit (least squares) to the measurements
𝑏 = 4 𝑎𝑡 𝑡 = −2, 𝑏 = 3 𝑎𝑡 𝑡 = −1, 𝑏 = 1 𝑎𝑡 𝑡 = 0, 𝑏 = 0 𝑎𝑡 𝑡 = 2
Then find the projection of b = (4,3,1,0) onto the column space of
1 −2
1 −1
𝐴=3
4
1 0
1 2