Share CPSC 284 - Exam 3 Review
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Describe the difference between a weak form of proof by induction and a strong form of proof by induction.
weak = assume true for specific k, then prove also true for k+1; strong = assume true for all k < n, then show it's also true for k+1
T/F: Every theorem can be proved using a single correct proof technique. (In other words, if you can prove theorem X using proof by contraction, that's the only proof that will work for that theorem. Any other techniques won't work.)
False
True/False: Given any 3 two-dimensional vectors A, B, and C, it's always possible to find a linear combination of A and B that is equal to C.
False
Normalize the vector newGuy = (1,4,5,2,8)
norm = 10.49 normalizedNewGuy = [0.09534626 0.38138504 0.47673129 0.19069252 0.76277007]
Suppose we have 3 vectors user1=(1,2,3,4,5) and user2=(7,6,1,8,2) and newGuy=(3,3,4,1,2). Which user has opinions more closely aligned with newGuy?
dot product of normed new user & normed user 1= 0.7557086549031783 vs dot product of normed new user & normed user 2 =0.7096921893772
When working with vectors the size and the length mean different things. What is another term that refers to the length of a vector?
norm/Euclidean norm
Suppose you have a set of vectors S, so far the values in S are {(1,2), (1,6)}. Identify an additional vector that you could add to S to ensure that the set S is linearly dependent.
absolutely any 2D vector
Is the vector [1 1] linearly independent, linearly dependent, both, or neither?
neither
Create a 4x4 matrix that is both symmetric and upper triangular but not an identity matrix.
Lots of possible answers. Here's one: (6,0,0,0) (0,5,0,0) (0,0,7,0) (0,0,0,3)
Is this possible and if so, what's the result?
column vector containing (29,29,33,44,25)
Find the adjacency matrix for this structure:
(1,1,0,0,1,0), (1,1,1,1,1,0), (0,1,1,1,0,1), (0,1,1,1,1,1), (1,1,0,1,1,1), (0,0,1,1,1,1)
