6) Given the matrix A [2-1 2-4] A 1 2-1 Lo a) Determine a basis for the null space of A b) What is the dimension of the null space of A? 7) Consider the following vectors: v= [1 2 1] w [-2 4 0] x 1 0.75] y [3 -1 1.25] a) Are v, w, x, and y, linearly independent? b) What is the dimension of the vector space spanned by v, w,x, and y? c) Determine a basis for the vector space spanned by v, w,x, and y

6) Given the matrix A [2-1 2-4] A 1 2-1 Lo a) Determine a basis for the null space of A b) What is the dimension of the null space of A? 7) Consider the following vectors: v= [1 2 1] w [-2 4 0] x 1 0.75] y [3 -1 1.25] a) Are v, w, x, and y, linearly independent? b) What is the dimension of the vector space spanned by v, w,x, and y? c) Determine a basis for the vector space spanned by v, w,x, and y

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.2: Orthogonal Complements And Orthogonal Projections

Problem 8EQ

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