= 2. Let P be the plane in R through the origin with normal vector n...

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= 2. Let P be the plane in R³ through the origin with normal vector n be the linear transformation such that L(7) is the projection of ✔ onto P. Let √₁ = 0 H -1 and B = {V₁, V2, ñ}. 2 2 (a) Show that {₁, ₂} is a basis of P. (b) Compute the RREF of the matrix V₂ -1 0 1 1 0 0 0 -1 2 0 1 0 1 2 1 0 0 1 121 2. Let L: R³ → R³ 1 H Do not show your work. 9 (c) Using part (a) or part (b), briefly explain why you can conclude that B is a basis of R³. (d) With & equal to the standard basis of R³, what are ŋ[id]ɛ and ɛ[id]Â? (e) Compute L(v₁), L(√₂), and L(ñ). (f) Compute [L]Â and [L]ɛ. = 2. Let P be the plane in R³ through the origin with normal vector n be the linear transformation such that L(7) is the projection of ✔ onto P. Let √₁ = 0 H -1 and B = {V₁, V2, ñ}. 2 2 (a) Show that {₁, ₂} is a basis of P. (b) Compute the RREF of the matrix V₂ -1 0 1 1 0 0 0 -1 2 0 1 0 1 2 1 0 0 1 121 2. Let L: R³ → R³ 1 H Do not show your work. 9 (c) Using part (a) or part (b), briefly explain why you can conclude that B is a basis of R³. (d) With & equal to the standard basis of R³, what are ŋ[id]ɛ and ɛ[id]Â? (e) Compute L(v₁), L(√₂), and L(ñ). (f) Compute [L]Â and [L]ɛ.