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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.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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
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