Show that (1, 0), (i, 0) ∈ C2 are linearly independent over R and linearly dependentover C

Question

Show that (1, 0), (i, 0) ∈ C2 are linearly independent over R and linearly dependentover C
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Solution 1

To show that the vectors (1, 0) and (i, 0) are linearly independent over R, we need to show that there are no real numbers a and b such that a*(1, 0) + b*(i, 0) = (0, 0).

If we set up the equation a*(1, 0) + b*(i, 0) = (0, 0), we get:

(a, 0) + (bi, 0) = (0, 0)

This simplifies to:

(a + bi, 0) = 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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