Please help me find the solution to these practices problems. Please show work and number the questions.

3: Let T: R\" > R3 be a linear transformation defined by x x1 x12x2+x3 T x: =x2+2x3+3x4. x 4 II I: Find the standard matrix of T. II: Find the dimension of the domain of T. III: Find the dimension of the range of T. IV: Find the dimension of the null space of T. V: Is T one-to-one? Explain why or why not? VI: ls T onto? Explain why or why not? VII: Is 1" an isomorphism? Explain why or why not? 4: Let ,: R2 - R3 be a linear transformation defined by )= 2x1 + 3x2] T1 X1 + X2 X1 - 2x2 And let 72: I3 - 12 be a linear transformation defined by X1 T2 X2 = X1 - 2x2 [2x1 + X3] I: Find the matrix representation of the composition To Tz Il: Find the matrix representation of the composition T2 0 T1