4. A linear transformation T: R R is given such that T(x, y, z) =...

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4. A linear transformation T: R³ → R³ is given such that T(x, y, z) = (2x+y+2z, 2x+3y + 4z,-x-y-z). a. Find I's transformation matrix according the following basis: E = {e₁ = (1,0,0), e₂ = (0,1,0), ez = (0,0,1)} . b. Find the second column if T's transformation matrix according the following basis: F = { ƒ₁ = (1,1,0), ƒ₂ = (1,0,1), ƒ3 = (0,1,1)} . 4. A linear transformation T: R³ → R³ is given such that T(x, y, z) = (2x+y+2z, 2x+3y + 4z,-x-y-z). a. Find I's transformation matrix according the following basis: E = {e₁ = (1,0,0), e₂ = (0,1,0), ez = (0,0,1)} . b. Find the second column if T's transformation matrix according the following basis: F = { ƒ₁ = (1,1,0), ƒ₂ = (1,0,1), ƒ3 = (0,1,1)} .