1. Given 4 5 U1 = -- > U2 = U3 = 0 1 (a) [4 points] Prove that ui, u2 and uz are linearly independent. (b) [8 points] Fi

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1 Given 4 5 U1 U2 U3 0 1 A 4 Points Prove That Ui U2 And Uz Are Linearly Independent B 8 Points Fi 1 (138.18 KiB) Viewed 22 times

1. Given 4 5 U1 = -- > U2 = U3 = 0 1 (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 u3. (c) [8 points] Let S = {u1, U2, U3} be a basis for a subspace V of R4. Transform S to an orthogonal basis for V by the Gram-Schmidt process.