Midterm 2 Theorems and Definitions Math 22a

Properties of Matrix Multiplication

Properties of Matrix Multiplication

Transpose

Invertible

When is a 2×2 matrix invertible?

What is the determinant of a 2×2 matrix?

Theorem: If A is an n by n invertible matrix….

Theorem about A and B are n x n matrices

Transpose example

How to express mxn matrix in subscript notation.

Key facts about invertible matrices.

Elementary Matrix

Note: The three elementary row ops. are:

1) Row switch
2) Row Multiplication
3) Row Addition

Good Strategy to find inverse of matrix.

nxn matrix A is invertible if and only if A is row equivalent to….

The invertible matrix theorem.

When is T invertible?

A matrix and its transpose have the same….

determinant