1. Consider the matrix [1 0 0 1 1 1] 1 10 21 3 A = 2 1 1 2 1 3 and the vector b [10 0 1 1 1 Let v1,.. V6 be the vectors given by columns 1, ...,6 of A. (a) Construct the augmented matrix [A|b] and use elementary row operations to reduce it to reduced echelon form. Show each step. (This row reduction can be used in almost everything that follows.) (b) Find a basis for the null space of A. (Hint: solve Ax = 0.) (c) Find a basis for the column space of A.

1. Consider the matrix [1 0 0 1 1 1] 1 10 21 3 A = 2 1 1 2 1 3 and the vector b [10 0 1 1 1 Let v1,.. V6 be the vectors given by columns 1, ...,6 of A. (a) Construct the augmented matrix [A|b] and use elementary row operations to reduce it to reduced echelon form. Show each step. (This row reduction can be used in almost everything that follows.) (b) Find a basis for the null space of A. (Hint: solve Ax = 0.) (c) Find a basis for the column space of A.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 2DE

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