Consider the function T : R R, defined by T(x, y, z) = (x + 3y,...

 

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Consider the function T : R R, defined by T(x, y, z) = (x + 3y, 2x + 5z) (a) Write the matrix for T. (b) For the vectors u = (1,5,-2), v = (2, 7, 4) = R, verify that T(2u+ 3v) = 2T(u) + 3T(v). (c) For the unit vectors i = (1, 0, 0), j = (0, 1, 0), k = (0, 0, 1), write the matrix [T] = [T(i) T(j)_T(k)] (i.e. write the matrix [T] whose columns are the vectors T(i), T(j), T(k)) Consider the function T : R R, defined by T(x, y, z) = (x + 3y, 2x + 5z) (a) Write the matrix for T. (b) For the vectors u = (1,5,-2), v = (2, 7, 4) = R, verify that T(2u+ 3v) = 2T(u) + 3T(v). (c) For the unit vectors i = (1, 0, 0), j = (0, 1, 0), k = (0, 0, 1), write the matrix [T] = [T(i) T(j)_T(k)] (i.e. write the matrix [T] whose columns are the vectors T(i), T(j), T(k)) Consider the function T : R R, defined by T(x, y, z) = (x + 3y, 2x + 5z) (a) Write the matrix for T. (b) For the vectors u = (1,5,-2), v = (2, 7, 4) = R, verify that T(2u+ 3v) = 2T(u) + 3T(v). (c) For the unit vectors i = (1, 0, 0), j = (0, 1, 0), k = (0, 0, 1), write the matrix [T] = [T(i) T(j)_T(k)] (i.e. write the matrix [T] whose columns are the vectors T(i), T(j), T(k))