(Solved): Let v1 = (2, 4, 1, 2), v2 = (1, 1, 1, 3), and v3 = (2, 1, 2, 1) in R 4 . 1. Find a vector u2 in the ...

Let v1 = (2, 4, 1, 2), v2 = (1, 1, 1, 3), and v3 = (2, 1, 2, 1) in R 4 .
1. Find a vector u2 in the span of v1 and v2 that's perpendicular to v1.
2. Find a vector u3 in the span of v1, v2 and v3 that's perpendicular to v1 and v2.
Explain why v1, u2, u3 are mutually perpendicular vectors with the same span as v1, v2, v3. Find the closest vector in the span of v1, v2, v3 to (2, 2, 1, 3).

= Problem 2. Let vi (2,4, 1, 2), v2 = (1, 1, 1, 3), and V3 = (2, 1, 2, 1) in R4. 1. Find a vector uz in the span of vi and v2 that's perpendicular to vi. 2. Find a vector uz in the span of v1, v2 and v3 that's perpendicular to vi and v2. Explain why V1, U2, U3 are mutually perpendicular vectors with the same span as V1, V2, V3, Find the closest vector in the span of V1, V2, V3 to (2,2,1,3).