Find a basis for and the dimension of the subspace W of R*. W = {(s + 5t, t, s, 3s - t): s andt are real numbers} (a) a basis for the subspace W of R4 (b) the dimension of the subspace W of R*

Find a basis for and the dimension of the subspace W of R. W = {(s + 5t, t, s, 3s - t): s andt are real numbers} (a) a basis for the subspace W of R4 (b) the dimension of the subspace W of R

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 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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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

Find a basis for and the dimension of the subspace W of R*.
W = {(s + 5t, t, s, 3s - t): s andt are real numbers}
(a) a basis for the subspace W of R4
(b) the dimension of the subspace W of R*

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