An m × n upper triangular matrix is one whose entries below the main diagonal are 0’s (...

An m × n upper triangular matrix is one whose entries below the main diagonal are 0’s (as in Exercise 8). When is a square upper triangular matrix invertible? Justify your answer.

Exercise 8:

Unless otherwise specified, assume that all matrices in these exercises are n × n. Determine which of the matrices in Exercises 1–10 are invertible. Use as few calculations as possible. Justify your answers.