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1. If S is the plane of vectors in R³ satisfying x₁ - x₂ + x3 = 0, write a basis for S¹. Construct a matrix that has S as its nullspace. 1b. What linear combination of v1 = (1, 1, -1) and v2 = (1, 0, 1) is the closest to b = (1, 1, 0).

1. If S is the plane of vectors in R³ satisfying x₁ - x₂ + x3 = 0, write a basis for S¹. Construct a matrix that has S as its nullspace. 1b. What linear combination of v1 = (1, 1, -1) and v2 = (1, 0, 1) is the closest to b = (1, 1, 0).

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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Please answer both a and b
1. If S is the plane of vectors in R³ satisfying x₁ - x2 + x3 = 0, write a basis for S¹. Construct a matrix that has S as its nullspace. 1b. What linear combination of v1 = (1, 1, -1) and v2 = (1, 0, 1) is the closest to b = (1, 1, 0). Text Predictions: On Accessibility: Good to go Display Settings Focus DA 1 and 1, adding to 2. But the correct dimensions rand n-r must add to n Σ i
Transcribed Image Text:1. If S is the plane of vectors in R³ satisfying x₁ - x2 + x3 = 0, write a basis for S¹. Construct a matrix that has S as its nullspace. 1b. What linear combination of v1 = (1, 1, -1) and v2 = (1, 0, 1) is the closest to b = (1, 1, 0). Text Predictions: On Accessibility: Good to go Display Settings Focus DA 1 and 1, adding to 2. But the correct dimensions rand n-r must add to n Σ i
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