Linear Algebra Question (Linear independence, subspace vectors span, linear combination)?
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Let v_1 = (1, 2, 2, 1), v_2 = (0, 2, 0, 1), v_3 = (-2, 0, -4, 3). a) Show that these vectors are linearly independent. b) What is the subspace of E^4 that they span, that is, given v = (y_1, y_2, y_3, y_4) how can we tell when v is a linear combination of v_1, v_2, and v_3? Please explain all steps. Thank you!
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Answer:
A * v_1 + B * v_2 = C * v_3. Show that A, B & C must equal 0 in order for this equation to be true.
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