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anonymous
 5 years ago
Subspace question: So in order for a subset S in vector space V to be a subspace it must have a nonempty set, closed under addition and scalar multiplication. What do they mean by nonempty set? How do you prove that it is nonempty?
anonymous
 5 years ago
Subspace question: So in order for a subset S in vector space V to be a subspace it must have a nonempty set, closed under addition and scalar multiplication. What do they mean by nonempty set? How do you prove that it is nonempty?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it must at least contain a zero element

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0non empty meaning there is at least one element in your vector space. , non empty is pretty self explanatory

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, i see that in most problems when they have an equation and its set equal to zero. Is it the same when they give you a MxN matrix? how do you know that it has the zero vector?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so for square matrices, nxn, the one all zeroes is your zero matrix

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For the most part I just assume that the subset is not empty and just rely on proving whether its closed under addition and scalar multiplication.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you should be able to identify the zero vector

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is important that you find or identify the zero vector when you are establishing a subspace, (a subset of your original vector space which is also a vector space in its own right)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, I know that my method of approaching these are wrong. I guess I am just thinking too much into it. Thanks for the help.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0:) why dont you write down a problem youre working on ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0V=Mn(Real), and S is the subset of all nxn lower triangular matrices.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the Mn is, M sub n and real is the real numbers symbol.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Express S in set notation and determine whether it is a subspace of the given vector space V.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Msubn means the set of nxn matrices

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so say we have [ 1 1 ] [ 2 2 ] , where [ 1 1 ] is the first row and [ 2 2 ] is the second row

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so whats a lower triangular matrix?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it would be [ 1 0 ] [ 1 2 ] for example

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0a better one would be [ 1 0 0 ] [ 1 2 0 ] [ 1 2 3 ] is a L T matrixx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok there are two conditions for a subspace , since we inherit the vector space properties from the fact that we are in the same set (subset)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you mind using twiddla

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so how would you find the zero vector, or better yet how would you know that ur dealing with an nonempty set?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0looool a lower triangular matrix is a matrix with all zeros below the major diagonal, whereas an upper triangular matrix has all zeros above the major diagonal. this definition might be a bit easier to see. One thing that is neat about these is that all you need to do to take the determinant of a matrix like this is multiply all numbers in the major diagonal. So if you had a test and you noticed the determinant of a matrix as mentioned by cantorset you could do that and you would spend a lot less time.
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