4. Find a basis for the span of{[1, 2, 1]", [3, 1, –1]", [1, –3, –3]"}

Given: uvw = 121, 31-1, 1-3-3 To find: The basis for the span. Concept Used: To find a basis for the…

Answered: 4. Find a basis for the span of {[1, 2,…

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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Question

4. Find a basis for the span of
{[1, 2, 1]", [3, 1, –1]", [1, –3, –3]"}

Expert Solution

Step 1: Given

Given:

$[\begin{matrix} u & v & w \end{matrix}] = [[\begin{matrix} 1 \\ 2 \\ 1 \end{matrix}], [\begin{matrix} 3 \\ 1 \\ - 1 \end{matrix}], [\begin{matrix} 1 \\ - 3 \\ - 3 \end{matrix}]]$

To find: The basis for the span.

Concept Used:

To find a basis for the span of set vectors, write the vectors as rows of the matrix and then reduce the matrix. The span of rows of a matrix is called row space of the matrix. The non-zero rows will be the basis of the matrix written as column matrix.

The column space is a space spanned by the columns of the initial matrix that corresponds to the pivot columns of the reduced matrix.

Row echelon form: A matrix is said to be in a row echelon form when all its non-zero rows have a pivot, that is, a non-zero entry such that all the entries to its left and below re equal to zero.