Texts: (2 points) For vectors vec(u)=[[5],[2]] and vec(v)=[[15],[-10]], the inner product of vec(u) and vec(v) is
A. 55
B. 65
C. 75
D. 85
(5 points) List the following vectors from greatest to least in terms of their magnitude.
A. [[1],[3],[-2]]
B. [[0],[4],[2],[1]]
C. [[2],[5]]
D. [[1],[0],[-2],[0],[1]]
E. [[0],[0],[0]]
(6 points) Consider the following set of vectors,
vec(u)_(1)=[[3],[-3],[0]], vec(u)_(2)=[[2],[2],[-1]], and vec(u)_(3)=[[1],[1],[4]]
First, verify that the given set is an orthogonal basis for R^(3). Then for vec(y)=[[5],[-3],[1]], find c_(1), c_(2), and c_(3) such that
vec(y) = c_(1)vec(u)_(1) + c_(2)vec(u)_(2) + c_(3)vec(u)_(3).
Consider the matrix A=[[1,0,-3,2],[0,1,-5,4],[3,-2,1,-2]].
(a) (4 points) Find a basis for ColA.
(b) (4 points) Find a basis for NullA.
1. (2 points) For vectors u = and v = [[15]], the inner product of u and v is 10.
A. 55
B. 65
C. 75
D. 85
2. (5 points) List the following vectors from greatest to least in terms of their magnitude.
A. [[1],[3],[-2]]
B. [[0],[4],[2],[1]]
C. [[2],[5]]
D. [[1],[0],[-2],[0],[1]]
E. [[0],[0],[0]]
3. (6 points) Consider the following set of vectors:
vec(u)_(1) = [[3],[-3],[0]]
vec(u)_(2) = [[2],[2],[-1]]
vec(u)_(3) = [[1],[1],[4]]
First, verify that the given set is an orthogonal basis for R^(3). Then for vec(y) = [[5],[-3],[1]], find c_(1), c_(2), and c_(3) such that
vec(y) = c_(1)vec(u)_(1) + c_(2)vec(u)_(2) + c_(3)vec(u)_(3).
4. Consider the matrix A = [[1,0,-3,2],[0,1,-5,4],[3,-2,1,-2]].
(a) (4 points) Find a basis for ColA.
(b) (4 points) Find a basis for NullA.