Answered: Let S = { (x, y, z, w) E R*; x – 2y + w…

Let S = { (x, y, z, w) E R*; x – 2y + w = 0 and 2x + z – w = 0 } . - Prove that S is a subspace by writing it as the null space of a matrix. S = null(A) where A = -1 1 2 2]

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 31EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn, W is the set...

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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 S = { (x, y, z, w) E R*; x – 2y + w = 0 and 2x + z – w =
Prove that S is a subspace by writing it as the null space of a matrix.
S = null(A)
where
A =
-1
-2
-1
1
2

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