4 −2 Problem1[20pts]Drawu= 1 ,w= 2 and(u+w),(u−w)inthe
plane.
Problem 2 [20pts] Find vectors u and w such that u + w = 5 and
2 u − w = 5.
8
Problem 3 [20pts] Find two nontrivial vectors u and w which are per- 1
pendicular to 0 and to each other. 1
Problem 4 [20pts] How long is the vector u = 1 ? 1
1
Problem 5 [20 pts] Consider the following system of equations:
(i) Apply Gauss Elimination in order to solve it;
2 x + 3 y + z = 8
4x + 7y + 5z = 20 − 2 y + 2 z = 0
(ii) Transform the above system of equations in matrix form and apply the Gauss Elimination in matrix form (indicate all matrices you used in the process).
1
