( a ) Express the vector e1 = [ 1 0 ] ( 2 * 1 vertical matrix ) as a linear combination of vector u and w . ( b ) Let T : R^2 - > R^3 be a linear transformation such that T ( u ) = [ 1 2 3 ] ( 3 * 1 vertical matrix ) and T ( w ) = [ 1 2 k ] ( 3 * 1 vertical matrix ) . Use your answer form part ( a ) to compute T (e1). ( c ) Find the standard matrix of T. ( d ) Let k = 0. Show that the equation T ( x ) = b does not have a solution for all possible b = [ b1 b2 b3 ] ( 3 * 1 vertical matrix ) , and describe the set of all b for which T ( x ) = b does have a solution . Does the answer change if k = 3 ?