Question: Let T : R 3 ? R 3 be defined by T ( x , y , z ) = ( x + 3 y

Let T : R3 ? R3 be defined by T (x, y, z) = (x + 3y + 3z,?3x ? 5y ? 3z,3x + 3y + z) . For v = (0,?1,4) find T(v) by:

a) Using the standard matrix

b) By using the matrix relative to B ={(1,?1,1),(?1,1,0),(?1,0,1)} and

B'={(?1,0,2),(0,?1,2),(?2,1,1)}.

Let T : R 3 ? R 3 be defined by T ( x , y , z ) =

Let T : R' -> R' be defined by T(x, y,z) =(x+3y+3z,-3x -5y- 3z, 3x + 3y+ z). For v = (0,-1,4) find T(v) by: Using the standard matrix b) By using the matrix relative to B = {(1,-1,1),(-1,1,0),(-1,0,1)} and B' = {(-1,0,2), (0,-1,2), (-2, 1, 1) }

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