Given v ? 0 and p in ?n, the line through p in the

Chapter 1, Problem 25E

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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).

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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).

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