Let a Find a basis u 1 , u 2 , u 3 for R 3 such that P is the change of coordinates matrix from u 1 , u 2 , u 3 to the basis v 1 , v 2 , v 3 Hint What do the columns of represent b Find a basis w 1 , w 2 , w 3 for R 3 such that P is the change of coordinates matrix from v 1 , v 2 , v 3 to w 1 , w 2 , w 3 P V 1 3 4 2 2 3 2 5 6 V 0 8 5 2 V3 2 6 P

Question: Let a. Find a basis {u 1 , u 2 , u 3 } for R 3 such that P is the change-of-coordinates matrix from

Let

P = V = 1 -3 4 -2 2 3 2 -5

a. Find a basis {u ₁, u ₂, u ₃} for R ³ such that P is the change-of-coordinates matrix from {u ₁, u ₂, u ₃} to the basis {v ₁, v ₂, v ₃}

[Hint: What do the columns of 6 V = 0 -8 5 2 V3 = 2 6 P represent?]

b. Find a basis {w ₁, w ₂, w ₃} for R ³ such that P is the change-of-coordinates matrix from {v ₁, v ₂, v ₃} to {w ₁, w ₂, w ₃}

P = V = 1 -3 4 -2 2 3 2 -5 6 V = 0 -8 5 2 V3 = 2 6 P -

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