Dimensions and Subspaces Help

Determine the dimensions of the following subspaces of R^2 and R^3?

1. R^3= span{(-2, -12, 10), (-1, 3, -4), (2, 3, -1)}
2. R^2= span{(–4, –2), (2, 0), (5, 0), (9, –1), (–2, 3)}
3. R^2= span{(7, –2), (–6, 5)}
4. R^2= span{(0, 0)}
5. R^3= span{(–20, –4, 8), (–1, –4, –2), (10, 2, –4), (–4, 3, 4)}
6. R^2= span{(–5, –7), (–6, 7, –8), (4, 8, –2)}


How would I go about doing this problem?

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Originally Posted by My Little Pony

1. R^3= span{(-2, -12, 10), (-1, 3, -4), (2, 3, -1)}
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How would I go about doing this problem?

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Vectors that span a subspace contain all the information you need to construct a basic for the subspace. Do you know how to calculate a basis of C(A)? If so, you should know that the columns of A span C(A). The columns of A can also a basis of C(A), but A is invertible (all columns are Linearly Independent).

In other words, construct a matrix having those vectors as columns and row-reduce. The dimension of their span is the number of non-zero rows you get.