Linear Algebra HW

Solve the following problems, showing any necessary work. Your answers must be exact, or must contain atleast four digits after the decimal point.

Note: Please handwrite it and make it clear>

MAT 242 Written Homework #6
1.A, 6.4, 6.A
Due: November 29

Solve the following problems, showing any necessary work. Your answers must be exact, or must contain at
least four digits after the decimal point.



 
 
−7 
0
−1



 −2   −5   1 
1. Let W be the subspace spanned by 
 . Note that this basis is not orthogonal.
,
,
9 
0
2



−12
10
4
 
5
 0
a. [1 point] Find the orthogonal projection of   into W.
10
15
b. [1 point] Find an orthogonal basis for W.
2. Find the best-fitting curve of each type below, using (−5, −214), (−1, −10), (0, −4), and (1, −4) for
data points.
a. [10 points] Lines: y = ax + b.
b. [10 points] Parabolas symmetric about the y-axis: y = ax2 + c.