Math 205b Quiz 09 - Lake Tahoe Community College, 2010
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1Quiz 09 page 1
04/02/2010
Math 205B
Name
1
1
13
2
4
12
1. Let A =
and y =
. It’s a fact that y is not in Col(A); you do not need to verify this.
4 16
5
5 25
21
1A. Find the least-squares solution of Ax = y. Show any and all matrices you used.
1B. Find the projection vector p of y onto the column space of A.
1C. Find the vector z satisfying p + z = y.
1D. Find the distance from y to Col(A).
⊥
1E. Verify that z is in Col(A)
by calculating the two appropriate dot products.
1F. The work done in this problem would be appropriate for solving which problem: (put a check next to the correct one)
2
Find the best fit curve of the form y = β
x + β
x
through the points (1, 1), (2, 4), (4, 16) and (5, 25).
1
2
2
Find the best fit curve of the form y = β
+ β
through the points (1, 13), (2, 12), (4, 5) and (5, 21).
x
0
1
2
Find the best fit curve of the form y = β
x + β
through the points (1, 13), (2, 12), (4, 5) and (5, 21).
x
1
2
2
Find the best fit curve of the form y = β
+ β
x + β
x
through the points (1, 1, 13), (2, 4, 12), (4, 16, 5) and (5, 25, 21).
0
1
2
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