Question: Linear Algebra Problem 2 (20 points) Consider the following three 3-vectors. Note that v1 + v2 v3 = 0. v1 = [0,1,1], vz = [1,0,1],

Linear Algebra

Problem 2 (20 points) Consider the following three 3-vectors. Note that v1 + v2 v3 = 0. v1 = [0,1,1], vz = [1,0,1], V3 = [1,1,2] 1. Give a basis for the column space of the matrix A = [v1 v2 V3 ]. 2. Find a basis for R3 that contains as many of the vectors v1. v2. and V3 as possible. If necessary, add in additional vectors. 3. Find a basis for the null space A. (Hint: Write the linear dependency of the three vectors as a matrix-vector product.) 4. Explain whetherthe function f where f(x) = Ax is one-to-one, onto, and/or invertible

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