Problem 7.2. (a) Given two vectors in R2 of coordinates (c-a, c2-a2) and (b1-a b2-a2), prove that they are linearly dependent iff 1 : |а1 b1 C1 а2 b2 С2 — 0. 1 1 (ь) Given three vectors in R3 of coordinates (dj—a1,dg-a2, dҙ — аз), (с1—ај, С2— а9, Сз —аз), and (b a b - a2, b3 - a3), prove that they linearly dependent iff are а1 bi C1 a2 b2 C2 d2 |аз бз Сз dз 1 d1 0. 1 1 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 7.2. (a) Given two vectors in R2 of coordinates (c-a, c2-a2) and (b1-a b2-a2),
prove that they are linearly dependent iff
1 :
|а1 b1 C1
а2 b2 С2 — 0.
1
1
(ь) Given three vectors in R3 of coordinates (dj—a1,dg-a2, dҙ — аз), (с1—ај, С2— а9, Сз —аз),
and (b a b - a2, b3 - a3), prove that they
linearly dependent iff
are
а1 bi C1
a2 b2 C2 d2
|аз бз Сз dз
1
d1
0.
1
1
1
Transcribed Image Text:Problem 7.2. (a) Given two vectors in R2 of coordinates (c-a, c2-a2) and (b1-a b2-a2), prove that they are linearly dependent iff 1 : |а1 b1 C1 а2 b2 С2 — 0. 1 1 (ь) Given three vectors in R3 of coordinates (dj—a1,dg-a2, dҙ — аз), (с1—ај, С2— а9, Сз —аз), and (b a b - a2, b3 - a3), prove that they linearly dependent iff are а1 bi C1 a2 b2 C2 d2 |аз бз Сз dз 1 d1 0. 1 1 1
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