Math 260, Fall 2018, Assignment 6

Mathematicians are like Frenchmen: whatever you say to them they translate into their own language, and forthwith it is something entirely different.

- Goethe

Read:

1. Section 2.4.

Carefully define the following terms, then give one example and one non-example of each:

1. Inverse (of a function from $\mathbb{R}^m$ to $\mathbb{R}^n$).

Carefully state the following theorems (you do not need to prove them):

1. Theorem concerning invertibility of non-square matrices.
2. Criterion for invertibility of a matrix, in terms of the reduced row-echelon form.
3. Criterion for invertibility of a square matrix, in terms of the rank.

Carefully describe the following algorithms:

1. Algorithm to determine whether a matrix is invertible, and to compute the inverse if it exists.

Solve the following problems:

1. Section 2.4, problems 1, 3, 5, 7, 9, 11, 17, and 21.

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