Prove that the set of vectors (1, 2), (3, 4) is linearly independent and spanning in R2

Question

Prove that the set of vectors (1, 2), (3, 4) is linearly independent and spanning in R2
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Solution 1

Sure, let's go through this step by step.

  1. Linear Independence: Two vectors are linearly independent if the only solution to the equation c1v1 + c2v2 = 0 is c1 = c2 = 0. Here, v1 = (1, 2) and v2 = (3, 4). So, we need to solve the following system of equations:

    c11 + c23 = 0 c12 + c24 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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