Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - 4.6 Rank of a Matrix and Systems of Linear Equations - 4.6 Exercises - Page 199: 20


(a) A basis for the column space is $$S=\{\left[1\right]\}.$$ (b) The rank of the matrix is $1$.

Work Step by Step

Given the matrix $$ \left[\begin{array}{lll}{1} & {2} & {3}\end{array}\right] $$ The reduced row echelon form is given by $$ \left[\begin{array}{lll}{1} & {2} & {3}\end{array}\right] $$ (a) A basis for the column space are the columns corresponding to the columns that have the leading 1's. That is, $$S=\{\left[1\right]\}.$$ (b) The rank of the matrix is $1$.
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