Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))

9th Edition

ISBN: 9780321962218

Author: Steven J. Leon

Publisher: PEARSON

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Textbook Question

Chapter 2.2, Problem 16E

A matrix A is said to be skew symmetric if A T = − A . For example,

A = [ 0 1 − 1 0 ]

is skew symmetric, since

A T = [ 0 − 1 1 0 ] = − A

If A is an n × n skew-symmetric matrix and n is odd, show that A must be singular.

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Chapter 2.2, Problem 15E

Chapter 2.2, Problem 17E

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Chapter 2 Solutions

Linear Algebra with Applications (9th Edition) (Featured Titles for Linear Algebra (Introductory))

Ch. 2.1 - Let A=[324123232] (a) Find the value of...Ch. 2.1 - Use determinants to determine whether the...Ch. 2.1 - Evaluate the following determinants: (a) |3523|...Ch. 2.1 - Evaluate the following determinants by inspection:...Ch. 2.1 - Evaluate the following determinant. Write your...Ch. 2.1 - Find all values of for which the following...Ch. 2.1 - Let A be a 33 matrix with a11=0 and a210 . Show...Ch. 2.1 - Write out the details of the proof of Theorem...Ch. 2.1 - Prove that if a row or a column of an nn matrix A...Ch. 2.1 - Use mathematical induction to prove that if A is...

Ch. 2.1 - Let A and B be 22 matrics. a) Does...Ch. 2.1 - Let A and B be 22 matrices and let C=[ a 11 a 12 a...Ch. 2.1 - Let A be a symmetric tridiagonal matrix (ie., A is...Ch. 2.2 - Evaluate each of the following determinants by...Ch. 2.2 - Let A=[0123111122331223] (a) Use the elimination...Ch. 2.2 - For each of the following, compute the determinate...Ch. 2.2 - Find all possible choices of c that would make the...Ch. 2.2 - Let Abe an nn matrix and a scalar. Show that...Ch. 2.2 - Let A be a nonsingular matrix. Show that...Ch. 2.2 - Let A and B be 33 matrices with det(A)=4 and...Ch. 2.2 - Show that if E is an elementary matrix, then ET is...Ch. 2.2 - Let E1,E2 , and E3 be 33 elementary matrices of...Ch. 2.2 - Let A and B be row equivalent matrices, and...Ch. 2.2 - Let Abe an nn matrix. Is it possible for A2+I=O in...Ch. 2.2 - Consider the 33 Vandermonde matrix V=[1 x 1 x 1 21...Ch. 2.2 - Suppose that a 33 matrix A factors into a product...Ch. 2.2 - Let A and B be nn matrices. Prove that the product...Ch. 2.2 - Let A and B be nn matrices. Prove that if AB=I ,...Ch. 2.2 - A matrix A is said to be skew symmetric if AT=A ....Ch. 2.2 - Let A be a nonsingular nn matrix with a nonzero...Ch. 2.2 - Let A be a kk matrix and let B be an (nk)(nk)...Ch. 2.2 - Let A and B be kk matrics and let M=[OBAO] Show...Ch. 2.2 - Show that evaluating the determinant of an nn...Ch. 2.2 - Show that the elimination method of computing the...Ch. 2.3 - For each of the following, compute (i) det(A) ,...Ch. 2.3 - Use the Cramer’s rule to solve each of the...Ch. 2.3 - Given A=[121043122] determine the (2, 3) entry of...Ch. 2.3 - Let A be the matrix in Exercise 3. Compute the...Ch. 2.3 - Prob. 5E Ch. 2.3 - If A is singular, what can you say about the...Ch. 2.3 - Prob. 7E Ch. 2.3 - Prob. 8E Ch. 2.3 - Prob. 9E Ch. 2.3 - Show that if A is nonsingular, then adj A is...Ch. 2.3 - Prob. 11E Ch. 2.3 - Prob. 12E Ch. 2.3 - Prob. 13E Ch. 2.3 - Prob. 14E Ch. 2.3 - Let x, y, and z be vectors in R3 . Show each of...Ch. 2.3 - Let x and y be vectors in R3 and define the skew...Ch. 2 - Generate random 55 matrices with integer entries...Ch. 2 - Prob. 2E Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - Prob. 5E Ch. 2 - Prob. 6E Ch. 2 - Prob. 1CTA Ch. 2 - For each statement that follows, answer true if...Ch. 2 - For each statement that follows, answer true if...Ch. 2 - Prob. 4CTA Ch. 2 - Prob. 5CTA Ch. 2 - For each statement that follows, answer true if...Ch. 2 - For each statement that follows, answer true if...Ch. 2 - Prob. 8CTA Ch. 2 - Prob. 9CTA Ch. 2 - Prob. 10CTA Ch. 2 - Let A and B he 33 matrices with det(A)=4 and...Ch. 2 - Prob. 2CTB Ch. 2 - Let A=[1111123413610141020] (a) Compute the LU...Ch. 2 - Prob. 4CTB Ch. 2 - Prob. 5CTB Ch. 2 - Prob. 6CTB Ch. 2 - Let A be an nn matrix and let be a scalar. Show...Ch. 2 - Prob. 8CTB Ch. 2 - Prob. 9CTB Ch. 2 - Let A be a matrix with integer entries. If...

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A matrix A is said to be skew symmetric if A T = − A . For example, A = [ 0 1 − 1 0 ] is skew symmetric, since A T = [ 0 − 1 1 0 ] = − A If A is an n × n skew- symmetric matrix and n is odd, show that A must be singular.

Solution Summary: The author states whether the given matrix is must be a singular. A is skew-symmetric if AT=-A.

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