Consider the alternative basis 7₁, 72, 73 of (column) vectors for R³ where: v₁ = e₁-e₂+€3, √¹₂ = 2 + ē3, 3 = e₁ +6₂ + €3. 1 Use row-reduction to compute B¹ where: | | B₁₂ V3 Use B to solve for the unknowns C₁, C₂, C3 in the two following cases: (i) a + be₂ + cez = C₁v₁ + C₂√¹₂ + C3V3. (ii) (a - b)ei + (b-c)₂+(a+b+c)ể3 = C₁v₁ +₂¹₂ + C3V3.
Consider the alternative basis 7₁, 72, 73 of (column) vectors for R³ where: v₁ = e₁-e₂+€3, √¹₂ = 2 + ē3, 3 = e₁ +6₂ + €3. 1 Use row-reduction to compute B¹ where: | | B₁₂ V3 Use B to solve for the unknowns C₁, C₂, C3 in the two following cases: (i) a + be₂ + cez = C₁v₁ + C₂√¹₂ + C3V3. (ii) (a - b)ei + (b-c)₂+(a+b+c)ể3 = C₁v₁ +₂¹₂ + C3V3.
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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Transcribed Image Text:Consider the alternative basis V₁, V2, V3 of (column) vectors for R³ where:
V₁=e₁ - e₂ + 23,
V₂ = €2+€3, V3 = e₁ + ē₂ + €3.
1
Use row-reduction to compute B where:
I
B: V₁ V2 V3
Use B -1 to solve for the unknowns C₁, C₂, C3 in the two following cases:
(i) ae + bez + cé3 = C₁V₁ + C₂0¹₂ + C3V3.
(ii) (a −b)ẻı+(b−c)ẻ?+(a+b+c)ẽ3=c+c+c33.
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