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Given three linearly independent vectors V₁ = (2, 10,0,3,7), V₂ = (-5,2,-3,3,-4), V3 = (-4,-5, -3,3,-10), in R5, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e; and e; then enter the values of i and j into the answer box below, separated with a comma.

Given three linearly independent vectors V₁ = (2, 10,0,3,7), V₂ = (-5,2,-3,3,-4), V3 = (-4,-5, -3,3,-10), in R5, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e; and e; then enter the values of i and j into the answer box below, separated with a comma.

Advanced Engineering Mathematics
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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Given three linearly independent vectors V₁ = (2, 10,0,3,7), V2 = (-5,2, -3,3,-4), V3 = (-4,-5, -3,3,-10), in R5, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e; and e; then enter the values of i and j into the answer box below, separated with a comma.
Transcribed Image Text:Given three linearly independent vectors V₁ = (2, 10,0,3,7), V2 = (-5,2, -3,3,-4), V3 = (-4,-5, -3,3,-10), in R5, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e; and e; then enter the values of i and j into the answer box below, separated with a comma.
Expert Solution
Step 1: Step 1

To complete the given three linearly independent vectors to a basis in ℝ5 using the first two standard basis vectors, we need to find two standard basis vectors, say ei and ej, that are linearly independent from the given vectors v1, v2, and v3.

First, let's check the linear independence of the given vectors:

Given vectors:

v1=(2,10,0,3,7)

v2=(−5,2,−3,3,−4)

v3=(−4,−5,−3,3,−10)

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