Question: 3. [2 points each] 1. Prove or disprove: the vectors vi = (2,311),v2 = (11 will) and v3 = (2,1,2) form a basis for R3.

3. [2 points each] 1. Prove or disprove: the vectors vi = (2,311),v2 = (11 will) and v3 = (2,1,2) form a basis for R3. 2. Find a basis for the subspace V := {031,2} E R3 |'.t + 23; 42 = l] }. 3. How man}r bases can a subspace have? 4. Let V be the set of vectors (3:, y, z, w) in R4 which are the solutions to the equa tions: 2.1: + 53; + 32: w 0 y 4:: 2w 2 0 63: 14y 133 + w 0 The subset V is a subspace of HF. Find a basis for V. (SUGGESTION: V is given as the set of solutions to a system of linear equations. You knowr how to paralneterize all the solutions. . . )

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