(Section 5.3) i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and v3 = (1,3,3,3) form a linearly dependent set in IR". ii. Express each vector in part i. as a linear combination of the other two. Prove that if {v₁, №₂, √3} is a linearly independent set of vectors, then so are (v₁,v3), and {₂}. a. b.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(Section 5.3)
3. a. i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and
√3 = (1,3,3,3) form a linearly dependent set in IR".
b.
ii. Express each vector in part i. as a linear combination of the other two.
Prove that if {v₁, 02, 03} is a linearly independent set of vectors, then so
are {vi, v3), and {₂}.
Transcribed Image Text:(Section 5.3) 3. a. i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and √3 = (1,3,3,3) form a linearly dependent set in IR". b. ii. Express each vector in part i. as a linear combination of the other two. Prove that if {v₁, 02, 03} is a linearly independent set of vectors, then so are {vi, v3), and {₂}.
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