. 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?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.2: Matrix Algebra

Problem 37EQ

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