Question

Consider the vectors, \(v_1 = \begin{pmatrix} 1 \\ 7 \\ -4 \end{pmatrix}, v_2 = \begin{pmatrix} -4 \\ -1 \\ 4 \end{pmatrix}, v_3 = \begin{pmatrix} r \\ 17 \\ -20 \end{pmatrix}\). a. For which value(s) of \(r\) are the vectors linearly independent? b. For which value(s) of \(r\) is \(v_3 \in \text{Span}\{v_1, v_2\}\)? If there is more than one value, use interval notation (e.g., \(x \le -1\) or \(x > 2\) is written \((-\infty, -1] \cup (2, +\infty)\)).

          Consider the vectors,
\(v_1 = \begin{pmatrix} 1 \\ 7 \\ -4 \end{pmatrix}, v_2 = \begin{pmatrix} -4 \\ -1 \\ 4 \end{pmatrix}, v_3 = \begin{pmatrix} r \\ 17 \\ -20 \end{pmatrix}\).
a. For which value(s) of \(r\) are the vectors linearly independent?
b. For which value(s) of \(r\) is \(v_3 \in \text{Span}\{v_1, v_2\}\)?
If there is more than one value, use interval notation (e.g., \(x \le -1\) or \(x > 2\) is written \((-\infty, -1] \cup (2, +\infty)\)).

Consider the vectors,
v1 =
< p m a t r i x >
, v2 =
< p m a t r i x >
, v3 =
< p m a t r i x >.
a. For which value(s) of r are the vectors linearly independent?
b. For which value(s) of r is v3 ∈Span{v1, v2}?
If there is more than one value, use interval notation (e.g., x ≤ -1 or x > 2 is written (-∞, -1] ∪ (2, +∞)).

Added by Heather L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Thanks for your feedback!

Consider the vectors, v_(1)=([1],[7],[-4]),v_(2)=([-4],[-1],[4]),v_(3)=([r],[17],[-20]) a. For which value(s) of r are the vectors linearly independent? b. For which value(s) of r is v_(3)inSpan{v_(1),v_(2)} ? If there is more than one value, use interval notation (e.g., x<=-1 or x>2 is written (-infty ,-1]cup (2,+infty ) Consider the vectors, 17 a. For which value(s) of r are the vectors linearly independent? b. For which value(s) of r is V3 E Span{V1,V2}? If there is more than one value, use interval notation (e.g., < --1 or > 2 is written (-00,-1]U (2,+)).