Let w, x, y, z be vectors and suppose z = -2x - 2y and wMark the statements below that must be true.A. Span(x, y)=Span(w)B. Span(x, y) = Span(x, w, z)C. Span(x, z)= Span(y, w)D. Span(y) = Span(w)2x + 4y + z.

Given are vectors and and .To choose which of the statements are true.A. B. C. D. The span of…

Answered: Let w, a,y, z be vectors and suppose z…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let w, x, y, z be vectors and suppose z = -2x - 2y and w
Mark the statements below that must be true.
A. Span(x, y)=Span(w)
B. Span(x, y) = Span(x, w, z)
C. Span(x, z)= Span(y, w)
D. Span(y) = Span(w)
2x + 4y + z.

Expert Solution

Step 1: Given

Given $open curly brackets w comma x comma y comma z close curly brackets$ are vectors and $z equals negative 2 x minus 2 y$ and $w equals 2 x plus 4 y plus z$ .

To choose which of the statements are true.

A. $s p a n open curly brackets x comma y close curly brackets equals s p a n open curly brackets w close curly brackets$

B. $s p a n open curly brackets x comma y close curly brackets equals s p a n open curly brackets x comma w comma z close curly brackets$

C. $s p a n open curly brackets x comma z close curly brackets equals s p a n open curly brackets y comma w close curly brackets$

D. $s p a n open curly brackets y close curly brackets equals s p a n open curly brackets w close curly brackets$

The span of some vectors $open curly brackets v subscript 1 comma v subscript 2 comma space... comma space v subscript n close curly brackets$ is the set of all possible linear combinations of the vectors $c subscript 1 v subscript 1 plus c subscript 2 v subscript 2 plus... plus c subscript n v subscript n$ where $c subscript 1 comma space c subscript 2 comma space... space comma space c subscript n$ are scalars.