Find the basis and dimension of the subspace. W = {(x,y,z): x,y,z ER and 2x+y+3z = 0) of a real vector space R

Question

Find the basis and dimension of the subspace. W = {(x,y,z): x,y,z ER and 2x+y+3z = 0) of a real vector space R
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Solution 1

The given subspace W is defined by the equation 2x + y + 3z = 0. We can rewrite this equation in terms of one variable, say y, to get y = -2x - 3z.

This means that any vector in W can be written in the form (x, -2x - 3z, z) = x(1, -2, 0) + z(0, -3, 1).

So, the vectors (1, -2, 0) and (0, -3, 1) f Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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

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