Let T: R R be the transformation given by the formula T([x, y, z])=[x -...

  

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Let T: R³ → R² be the transformation given by the formula T([x, y, z])=[x - y, y - z]. 1. Show that T is a linear transformation. 2. Find the matrix A such that T(X) = AX for all X = [x, y, z]t € R³. 3. Find the matrix representation B of T with respect to ordered bases u= {[1, 0, 0], [0, 1, 0], [1, 1, 1]} of R³ and V = {[1,1],[1, 0]} of R². Let T: R³ → R² be the transformation given by the formula T([x, y, z])=[x - y, y - z]. 1. Show that T is a linear transformation. 2. Find the matrix A such that T(X) = AX for all X = [x, y, z]t € R³. 3. Find the matrix representation B of T with respect to ordered bases u= {[1, 0, 0], [0, 1, 0], [1, 1, 1]} of R³ and V = {[1,1],[1, 0]} of R².