(adsbygoogle = window.adsbygoogle || []).push({}); Given: V={(1,1,3,2),(-1,2,1,-4),(0,3,4,-2)}; w=(-1,5,12,-9)

1) determine whether the given vector w belongs to Sp(V);

2) use the row reduction from 1) to explain whether or not V is a basis for Sp(V);

3) if V is a basis for Sp(V), and w is in Sp(V), determine, (w)[v], where [v] denotes a subscript.

For 1) I am not very sure about the Sp(V)..Am I supposed to make an augmented matrix of V and w and reduce it RREF, and then go from there? Say, if the result is consistent, then it belongs to Sp(V)?

By the definition of a basis, I need to show that V is linearly independent and is a spanning set for Sp(V) (?). How to show V is a spanning set of itself? Since it's Sp(V), is V already a spanning set of Sp(V)?

Suppose that V is a basis for Sp(V) and w is in SP(V), do I write V and w as an augmented matrix and solve straight away for (w)[v]?

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# Determine whether or not a vector belongs to a Sp(V) and so on

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