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Given v ? 0 and p in ?n, the line through p in the
Chapter 1, Problem 25E(choose chapter or problem)
PROBLEM 25E
Given v ≠ 0 and p in ℝn, the line through p in the direction of v has the parametric equation x = p + t v. Show that a linear transformation T: ℝn → ℝn. maps this line onto another line or onto a single point (a degenerate line).
Questions & Answers
QUESTION:
PROBLEM 25E
Given v ≠ 0 and p in ℝn, the line through p in the direction of v has the parametric equation x = p + t v. Show that a linear transformation T: ℝn → ℝn. maps this line onto another line or onto a single point (a degenerate line).
ANSWER:
Solution
Step 1:
Given: v ≠ 0 and p in ℝn, the line through p in the direction of v has the parametric equation x = p + t v
We have to Show that a linear transformation T: ℝn → ℝn. maps this line onto another line or onto a single point (a degenerate line).