Let and i = Compute the area of the parallelogram determined by four points with position vectors ū, ö, ü + ö,ō. Compute the determinant of the 2 × 2 matrix [ü, ü]. How do they compare? Replace the first entry of v by an arbitrary number z, 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 v is changed to I.
Let and i = Compute the area of the parallelogram determined by four points with position vectors ū, ö, ü + ö,ō. Compute the determinant of the 2 × 2 matrix [ü, ü]. How do they compare? Replace the first entry of v by an arbitrary number z, 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 v is changed to I.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 70E: The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six...
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![Let
and
ปี -
Compute the area of the parallelogram determined by four points with
position vectors i, v, ủ +0,0. Compute the determinant of the 2 × 2 matrix
[ū,0]. How do they compare? Replace the first entry of i by an arbitrary
number z, 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 v is changed to .
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Transcribed Image Text:Let
and
ปี -
Compute the area of the parallelogram determined by four points with
position vectors i, v, ủ +0,0. Compute the determinant of the 2 × 2 matrix
[ū,0]. How do they compare? Replace the first entry of i by an arbitrary
number z, 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 v is changed to .
||
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