1. Given 2 U1 - u2 = 3 1 U3 同 (a) [4 points] Prove that ui, u2 and uz are linearly independent. (b) [8 points] Find all

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1. Given 2 U1 - u2 = 3 1 U3 同 (a) [4 points] Prove that ui, u2 and uz are linearly independent. (b) [8 points] Find all unit vectors p E R4 (i.e., length/norm of p is 1) so that p is orthogonal to ui, u2 and us ©) [8 points] Let S = {41, 42, 43 } be a basis for a subspace V of R4. Transform S to an orthogonal basis for V by the Gram-Schmidt process.