Homework Help is Here – Start Your Trial Now!
Math
Algebra
Let A be the matrix consisting of columns equal to the given vectors. A = [w, | w] -1 5 -4 -2 Then the subspace W spanned by the vectors w, and w, is the same as the subspace spanned by the columns of A. By definition, this says that W is the column space of A. Recall that in this case, this means that the orthogonal complement of W is the null space of AT. That is, w- = null(AT). Thus, we must find this null space. First, find AT. 5 -2 AT = 1. Write the augmented matrix and use row operations to reduce. 5 -2 1. -4 1 -4 1.

Let A be the matrix consisting of columns equal to the given vectors. A = [w, | w] -1 5 -4 -2 Then the subspace W spanned by the vectors w, and w, is the same as the subspace spanned by the columns of A. By definition, this says that W is the column space of A. Recall that in this case, this means that the orthogonal complement of W is the null space of AT. That is, w- = null(AT). Thus, we must find this null space. First, find AT. 5 -2 AT = 1. Write the augmented matrix and use row operations to reduce. 5 -2 1. -4 1 -4 1.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 59CR
See similar textbooks
icon
Related questions
Question

please box in correct order so I can learn clearly. thank you.

Let A be the matrix consisting of columns equal to the given vectors. A = [w, | w,] -1 5 -4 -2 1 Then the subspace W spanned by the vectors w, and w, is the same as the subspace spanned by the columns of A. By definition, this says that W is the column space of A. Recall that in this case, this means that the orthogonal complement of W is the null space of A". That is, w = null(A"). Thus, we must find this null space. First, find AT. 1 -2 AT = 1 -4 Write the augmented matrix and use row operations to reduce. 5 -2 = 1 -4 1 -1 1 -4
Transcribed Image Text:Let A be the matrix consisting of columns equal to the given vectors. A = [w, | w,] -1 5 -4 -2 1 Then the subspace W spanned by the vectors w, and w, is the same as the subspace spanned by the columns of A. By definition, this says that W is the column space of A. Recall that in this case, this means that the orthogonal complement of W is the null space of A". That is, w = null(A"). Thus, we must find this null space. First, find AT. 1 -2 AT = 1 -4 Write the augmented matrix and use row operations to reduce. 5 -2 = 1 -4 1 -1 1 -4
Let W be the subspace spanned by the given vectors. Find a basis for wt. -1 1 W2 -4 -2
Transcribed Image Text:Let W be the subspace spanned by the given vectors. Find a basis for wt. -1 1 W2 -4 -2
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS