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How to determine if vectors span r3

2 Answers Sorted by: 2 First check if the vectors are linearly independent. You can do this by putting the matrix [ 1 2 1 3 − 1 − 4 0 7 7] into reduced row echelon form. This gives

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Linear Dependence and Span

This video explains how to determine if a given vector in R3 is in the span two other vectors in R3.

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Algebra

How to determine whether a set spans in Rn

One way to check is to make all 3x3 matrices from any 3 of the 4 vectors. If the determinant of any one of these matrices is #0, then those 3 vectors span R3 since they are linearly

Span and linear independence example

If you have 3 linearly independent vectors, they will span a 3 -dimensional space. If you have 3 vectors that are linearly dependent, they will span a space of 0, 1, or 2 dimensions.

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8.1 Span of a Set of Vectors

At this point, it is clear the rank of the matrix is 3, so the vectors span a subspace of dimension 3, hence they span R 3. See if one of your vectors is a linear combination of the others. If so, you

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How do I determine if a set of vectors spans a space?

Determine if the vectors v 1 = (3,1,4), v 2 = (2,-3,5), v 3 = (5,-2,9), v 4 = (1,4,-1) span ℝ 3 Homework Equations The Attempt at a Solution So I first arranged it as a matrix, Now I know