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. A matrix is said to be skew symmetric if A = -AT. Thus skew symmetric, while is not. is a. Show that all the diagonal elements of a skew symmetric matrix are equal to zero. b. Let A be a 3 x 3 skew symmetric matrix. Show that det(A) = 0. c. If A is a 2 × 2 skew symmetric matrix, must det(A) = 0? d. What happens if A is an n x n skew symmetric matrix?

. A matrix is said to be skew symmetric if A = -AT. Thus skew symmetric, while is not. is a. Show that all the diagonal elements of a skew symmetric matrix are equal to zero. b. Let A be a 3 x 3 skew symmetric matrix. Show that det(A) = 0. c. If A is a 2 × 2 skew symmetric matrix, must det(A) = 0? d. What happens if A is an n x n skew symmetric matrix?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 7CR
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. A matrix is said to be skew symmetric if A = -AT. Thus skew symmetric, while is not. is a. Show that all the diagonal elements of a skew symmetric matrix are equal to zero. b. Let A be a 3 x 3 skew symmetric matrix. Show that det(A) = 0. c. If A is a 2 × 2 skew symmetric matrix, must det(A) = 0? d. What happens if A is an n x n skew symmetric matrix?
Transcribed Image Text:. A matrix is said to be skew symmetric if A = -AT. Thus skew symmetric, while is not. is a. Show that all the diagonal elements of a skew symmetric matrix are equal to zero. b. Let A be a 3 x 3 skew symmetric matrix. Show that det(A) = 0. c. If A is a 2 × 2 skew symmetric matrix, must det(A) = 0? d. What happens if A is an n x n skew symmetric matrix?
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