Is the vector [1 1] linearly independent, linearly dependent, both, or neither?
neither
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10
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
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heart
Other team wins 20 points!
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shark
Other team loses 20 points!
Okay!
fairy
Take points!
5
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25
banana
Go to last place!
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thief
Give points!
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25
gift
Win 10 points!
Okay!
rocket
Go to first place!
Okay!
thief
Give points!
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10
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
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15
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
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
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lifesaver
Give 15 points!
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shark
Other team loses 15 points!
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shark
Other team loses 25 points!
Okay!
baam
Lose 20 points!
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10
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)
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10
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
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10
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.
