[M] In Exercises 37–40, let T be the linear transformation whose standard matrix is given....

[M] In Exercises 37–40, let T be the linear transformation whose standard matrix is given. In Exercises 37 and 38, decide if T is a one-to-one mapping. In Exercises 39 and 40, decide if T maps ℝ⁵ onto ℝ⁵. Justify your answers.