3 and v = Compute the area of the parallelogram determined by four points with position vectors ū, ī, ū + ū, 0. Compute the determinant of the 2 x 2 matrix [ū, v]. How do they compare? Replace the first entry of v by an arbitrary number a, and repea the problem. Draw a picture of both parallelograms and explain geometrically what happens to the area of the parallelogram

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 10AEXP
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Question 1: Let
i =
and
Compute the area of the parallelogram determined by four
points with position vectors ū, ī, ū + v, 0. Compute the
determinant of the 2 × 2 matrix [ū, ū]. How do they compare?
Replace the first entry of v by an arbitrary number æ, and repeat
the problem. Draw a picture of both parallelograms and explain
geometrically what happens to the area of the parallelogram
when the first coordinate of i is changed to x.
||
Transcribed Image Text:Question 1: Let i = and Compute the area of the parallelogram determined by four points with position vectors ū, ī, ū + v, 0. Compute the determinant of the 2 × 2 matrix [ū, ū]. How do they compare? Replace the first entry of v by an arbitrary number æ, and repeat the problem. Draw a picture of both parallelograms and explain geometrically what happens to the area of the parallelogram when the first coordinate of i is changed to x. ||
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