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Exercise Set 1: Write the matrix A from the given vectors. Calculate the area (or volume) of the parallelogram (parallelepiped) defined by them. (a) ū= (1,4), v = (5,0) (b) u = (3,2), v = (6,—4) (c) u = (2,5, 0), v = (3,−2, −1), w = (−1, 4, 3) (d) u = the vector starting at the point (2, 4) and ending at the point (5, 11),

Exercise Set 1: Write the matrix A from the given vectors. Calculate the area (or volume) of the parallelogram (parallelepiped) defined by them. (a) ū= (1,4), v = (5,0) (b) u = (3,2), v = (6,—4) (c) u = (2,5, 0), v = (3,−2, −1), w = (−1, 4, 3) (d) u = the vector starting at the point (2, 4) and ending at the point (5, 11),

Elementary Linear Algebra (MindTap Course List)
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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Area Theorem: If A is a 2 x 2 matrix, the area of the parallelogram determined by the columns of A is the absolute value of the determinant of A, Area = |det (A)]. The same formula calculates the volume of the parallelepiped determined by the columns of A, if A is a 3 x 3 matrix. Example: The vectors ū = (2,1), ✓ = (3,0) define the parallelogram 0 u V 2 3 4 A = = [²3], det A = −3, |det(A)| = |–3| = 3 5 Exercise Set 1: Write the matrix A from the given vectors. Calculate the area (or volume) of the parallelogram (parallelepiped) defined by them. (a) u = (1,4), v = = (5,0) (b) u = (3,2), v = (6,-4) (c) u = (2,5, 0), v = (3,−2,−1), w = (–1,4,3) (d) u = the vector starting at the point (2, 4) and ending at the point (5, 11), ✓ = the vector starting at the point (2,4) and ending at the point (-4,5). For this part include a graph of the points, vectors, and parallelogram.
Transcribed Image Text:Area Theorem: If A is a 2 x 2 matrix, the area of the parallelogram determined by the columns of A is the absolute value of the determinant of A, Area = |det (A)]. The same formula calculates the volume of the parallelepiped determined by the columns of A, if A is a 3 x 3 matrix. Example: The vectors ū = (2,1), ✓ = (3,0) define the parallelogram 0 u V 2 3 4 A = = [²3], det A = −3, |det(A)| = |–3| = 3 5 Exercise Set 1: Write the matrix A from the given vectors. Calculate the area (or volume) of the parallelogram (parallelepiped) defined by them. (a) u = (1,4), v = = (5,0) (b) u = (3,2), v = (6,-4) (c) u = (2,5, 0), v = (3,−2,−1), w = (–1,4,3) (d) u = the vector starting at the point (2, 4) and ending at the point (5, 11), ✓ = the vector starting at the point (2,4) and ending at the point (-4,5). For this part include a graph of the points, vectors, and parallelogram.
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