c) Consider the vector X₁. -3 = [³3] i. Express x₁ as a linear combination of the standard basis vectors e₁and e₂. Perform a change of basis on x₁ to the basis vectors b₁and b₂. ii. iii. X1 = b₁ = [₁], b₂ = [¹,₁] Draw a diagram to illustrate the vector x₁ with respect to both basis sets.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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c) Consider the vector X₁.
i.
ii.
iii.
[3]
Express x₁ as a linear combination of the standard basis vectors e₁and e₂.
Perform a change of basis on x₁to the basis vectors b₁and b₂.
X₁ =
b₁ = [1], b₂ = [_-¹₁].
Draw a diagram to illustrate the vector x₁ with respect to both basis sets.
Transcribed Image Text:c) Consider the vector X₁. i. ii. iii. [3] Express x₁ as a linear combination of the standard basis vectors e₁and e₂. Perform a change of basis on x₁to the basis vectors b₁and b₂. X₁ = b₁ = [1], b₂ = [_-¹₁]. Draw a diagram to illustrate the vector x₁ with respect to both basis sets.
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