2.3 Span of a Set of Vectors
Reading
Try out the preview activity and read Chapter 2 Section 3 in Understanding Linear Algebra by David Austin.
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We begin with a few examples of checking if a vector is in the span of a set of vectors.
Finally we look at ways to describe the span of a set of vectors:
Proposition
Consider:
Is the vector [latex]\vec{v}=\begin{bmatrix} \pi\\e\end{bmatrix}[/latex] in the span of {[latex]\begin{bmatrix} 1\\ 2 \end{bmatrix}[/latex], [latex]\begin{bmatrix} 2 \\1 \end{bmatrix}[/latex]}? Describe this span.
Is the vector [latex]\vec{v}= \begin{bmatrix} 2 \\ 3 \\ 5 \end{bmatrix}[/latex] in the span of {[latex]\begin{bmatrix} 4 \\ 6 \\ 10 \end{bmatrix}[/latex], [latex]\begin{bmatrix} 1 \\ 0 \\ 2\end{bmatrix}[/latex]}? Describe this span.