Consider the vectors u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = = [1,0,3]. (a) Show that the vectors u₁, u₂ and u3 are linearly independent. (b) Show that the vector v is in the span of u₁, U₂ and u3. (c) Find the coordinate vector of v with respect to {U₁, U2, U3}. (d) Write the zero vector as as a non-trivial linear combination of the vectors u₁, U2, U3 and w.
Consider the vectors u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = = [1,0,3]. (a) Show that the vectors u₁, u₂ and u3 are linearly independent. (b) Show that the vector v is in the span of u₁, U₂ and u3. (c) Find the coordinate vector of v with respect to {U₁, U2, U3}. (d) Write the zero vector as as a non-trivial linear combination of the vectors u₁, U2, U3 and w.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the vectors
u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = = [1,0,3].
(a) Show that the vectors u₁, u₂ and u3 are linearly independent.
(b) Show that the vector v is in the span of u₁, U₂ and u3.
(c) Find the coordinate vector of v with respect to {U₁, U2, U3}.
(d) Write the zero vector as as a non-trivial linear combination of the vectors u₁, U2, U3
and w.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F110c967c-36b0-4d8b-a5d1-a7f4ac9604c9%2Fdc3709fc-aaec-40b7-9085-f760335c9670%2F7soo7eq_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the vectors
u₁ = [1,0,−1], _U2 = [1,0,0] and u3 = [0, 1, 1], v = [5, 1, 3] and w = = [1,0,3].
(a) Show that the vectors u₁, u₂ and u3 are linearly independent.
(b) Show that the vector v is in the span of u₁, U₂ and u3.
(c) Find the coordinate vector of v with respect to {U₁, U2, U3}.
(d) Write the zero vector as as a non-trivial linear combination of the vectors u₁, U2, U3
and w.
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