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October 2nd, 2018, 09:10 PM   #1
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Linear Combinations

Write the following statement in formal mathematical notation, including the sigma notation:
a. Any linear combination of a finite number of linear combinations of a given set of vectors {x1,x2,...,xn}, generates a linear combination of the given set of vectors.

b. Prove the statement in part a.
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October 2nd, 2018, 09:52 PM   #2
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Write the following statement in formal mathematical notation ...
Is that an order?
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October 2nd, 2018, 10:00 PM   #3
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Is that an order?
No I am so sorry, I did not mean it to come off like that. I'm going to be honest, this is part of my homework that I have no idea how to do/start. I finished the rest of the homework but am now stuck on this problem and am now starting to get desperate.

Last edited by skipjack; October 3rd, 2018 at 01:22 AM.
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October 2nd, 2018, 10:39 PM   #4
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a. Any linear combination of a finite number of linear combinations of a given set of vectors {x1,x2,...,xn}, generates a linear combination of the given set of vectors.
The first thing to do is unpack that convoluted statement which seems to be deliberately obfuscated. Did you copy it down exactly as given?

So working right to left, we have a finite set of vectors $x_i$. Then we have linear combinations of those: that is, expressions of the form ________. I'll let you fill that in; since you should be able to do that.

And then we have a linear combination (the word finite is redundant since linear combinations are finite by definition) of those other linear combinations. And we are asked if that expression is in fact a linear combination of the original vectors.

Does this help? The trick is to read the statement very carefully to understand what it means.

Last edited by Maschke; October 2nd, 2018 at 10:45 PM.
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October 3rd, 2018, 01:37 AM   #5
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. . . am now starting to get desperate.
Calmly do a web search for a key phrase, such as "linear combination".
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