Math 121: Linear Algebra and Applications
Solution Set 3
Exercise 1 (1.6/35).
(a) Let v + W be a typical element of V /W . Since v V , we can write it as
v = a1 u1 + . . . + ak uk + ak+1 uk+1 + . . .
Math 121: Linear Algebra and Applications
Solution Set 2
Exercise 1 (1.4/12).
Recall that for if and only if statements we need to prove both directions: assuming the
statement to the left prove the o
Solutions
Midterm 1 for Math 121
1. (20 points)
a) True
b) False
c) False
d) True
e) True
2. (40 points)
a) Clearly, the zero vector lies in each of the subsets in (i), (ii). Thus, check if for any tw
Midterm 2 for Math 121
Last Name:
First Name:
Apart from question 1, you must fully justify your answers. On this exam the full
score is 100 points.
You may assume all vector spaces are nite-dimension
Math 121: Linear Algebra and Applications
Solution Set 1
Exercise 1.
(a) TRUE. This is one of the vector space axioms (VS 3).
(b) FALSE. We proved this in class but here is a short proof. Suppose ther
Solutions
Midterm 2 for Math 121
1. (20 points)
a) False
b) False
c) False
d) False
e) True
2. (50 points)
a) (30 points)
2 2
A = 1 2
2 2
3
1
1
First, we compute the characteristic polynomial pA ().
Math 121: Linear Algebra and Applications
Solution Set 6
Exercise 1 (2.6/1d-h, 2.7/1c-g).
(a) (d) TRUE. Note that for any nite dimensional V , V = (V )
(e) FALSE. Let V = R3 and consider the standard
Midterm 1 for Math 121
3 pages (including this one)
Last Name:
First Name:
Apart from question 1, you must fully justify your answers. On this exam the full
score is 100 points.
You may assume all vec