Problem: The linear map T from 3-dimensional x-space to 3-dimensional y-space is defined by y = T(x) = Ax with Y1 = x1 + 5x2 + 4x3 Y2 = 2x1 + 6x2 + 2x3 Y3 = 3x1 + 7x2 (i) Use row reduction for Ax=y to show that R(T) = Col(A) is given by one linear homogeneous equation for y1, y2, Y3. (ii) Find all vectors which are perpendicular (orthogonal) to R(T). (iii) Determine the null space of the transpose of A. (iv) Find an orthogonal basis for R(T).