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Suppose x, y e R" are nonparallel vectors. (Recall the definition on p. 3.) a. Prove that if sx +ty = 0, then s = t = 0. (Hint: Show that neither s #0 nor t # 0 is possible.) b. Prove that if ax + by = cx +dy, then a = c and b= d.

Suppose x, y e R" are nonparallel vectors. (Recall the definition on p. 3.) a. Prove that if sx +ty = 0, then s = t = 0. (Hint: Show that neither s #0 nor t # 0 is possible.) b. Prove that if ax + by = cx +dy, then a = c and b= d.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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25. Suppose x, y e R" are nonparallel vectors. (Recall the definition on p. 3.) a. Prove that if sx + ty = 0, then s = t = 0. (Hint: Show that neither s + 0 nor t + 0 is possible.) b. Prove that if ax + by = cx + dy, then a = c and b = d.
Transcribed Image Text:25. Suppose x, y e R" are nonparallel vectors. (Recall the definition on p. 3.) a. Prove that if sx + ty = 0, then s = t = 0. (Hint: Show that neither s + 0 nor t + 0 is possible.) b. Prove that if ax + by = cx + dy, then a = c and b = d.
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