A set of two, three, or four red vectors in R2 or R³ is shown in each picture below. Determine whether each set of vectors is a basis (for the appropriate subspace, R2 or R³). Note: For the pictures in R³, a grid is drawn in the xy-plane, and vectors with their tip on the grid are in the xy-plane, while vectors with their tip not on the grid are not in the xy-plane. Y I not a basis v I not a basis Y basis not a basis X basis not a basis v Y X

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A set of two, three, or four red vectors in R2 or R³ is shown in each picture below. Determine whether each set of vectors is a basis (for the
appropriate subspace, R² or R³). Note: For the pictures in R³, a grid is drawn in the xy-plane, and vectors with their tip on the grid are in
the xy-plane, while vectors with their tip not on the grid are not in the xy-plane.
Y
I
not a basis v
I
not a basis
Y
basis
not a basis
X
basis
not a basis v
Y
X
Transcribed Image Text:A set of two, three, or four red vectors in R2 or R³ is shown in each picture below. Determine whether each set of vectors is a basis (for the appropriate subspace, R² or R³). Note: For the pictures in R³, a grid is drawn in the xy-plane, and vectors with their tip on the grid are in the xy-plane, while vectors with their tip not on the grid are not in the xy-plane. Y I not a basis v I not a basis Y basis not a basis X basis not a basis v Y X
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