MATH 136 - Assignment 3
Due Wednesday May 28 at 8:30am in the assignment dropbox
2
1
1. Let u = 1 , v = 2 . Evaluate the following.
3
1
(a) u v
(b) projv u
(c) perpv u
(d) proju v
(e) perpu v
1
2
2. Consider the plane S = Span 1 , 1 in R3 .
1
1
(a) Fi
MATH 136 - Assignment 2
Due Wednesday May 21 at 8:30am in the assignment dropbox
1. Let c = 0 be a real constant and v1 , . . . , vk Rn .
Prove that Span(v1 , . . . , vk ) = Span(v1 , . . . , vi1 , cvi , vi+1 , . . . , vk ).
2. Prove whether the following
MATH 136 - Assignment 2
Due Wednesday May 21 at 8:30am in the assignment dropbox
1. Let c = 0 be a real constant and v1 , . . . , vk Rn .
Prove that Span(v1 , . . . , vk ) = Span(v1 , . . . , vi1 , cvi , vi+1 , . . . , vk ).
Solution: Let x Span(v1 , . .
MATH 136 - Assignment 1
Due Wednesday May 14 at 8:30am in the assignment dropbox
1. Compute each of the following linear combinations.
(a)
1
3
4
5
+
5
4
2
3
3
+3
(b) 3
5
2
(c) 2 3 3
1
2
15
3
13
0 + 6
2
8
2. Describe geometrically the following sets a