Show that W = {(x1, x2, x3, x4)|x4 − x3 = x2 − x1} is a subspace of R4, spanned by (1, 0, 0, −1), (0, 1, 0, 1) and (0, 0, 1, 1)

Question

Show that W = {(x1, x2, x3, x4)|x4 − x3 = x2 − x1} is a subspace of R4, spanned by (1, 0, 0, −1), (0, 1, 0, 1) and (0, 0, 1, 1)

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Solution 1

To show that W is a subspace of R4, we need to prove that it satisfies three properties:

The zero vector of R4 is in W.
W is closed under vector addition.
W is closed under scalar multiplication.
The zero vector in R4 is (0,0,0,0). If we substitute these values into the equation x4 - Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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