Let W be the subspace of R5 spanned by the following vectors: u1=(1,2,1,3,2), u2=(1,3,3,5,3), u3=(3,8,7,13,8), u4=(1,4,6,9,7), u5=(5,13,13,25,19) Find a basis of W consisting of the original given vectors and find dim W.

Let W be the subspace of R5 spanned by the following vectors: u1=(1,2,1,3,2), u2=(1,3,3,5,3), u3=(3,8,7,13,8), u4=(1,4,6,9,7), u5=(5,13,13,25,19) Find a basis of W consisting of the original given vectors and find dim W.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Let W be the subspace of R⁵spanned by the following vectors:

u₁=(1,2,1,3,2),

u₂=(1,3,3,5,3),

u₃=(3,8,7,13,8),

u₄=(1,4,6,9,7),

u₅=(5,13,13,25,19)

Find a basis of W consisting of the original given vectors and find dim W.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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