# Chapter 22: Matrices 2 Flashcards

## Determinants, inverse matrices, linear equations, manipulating determinants, and eigen-everything. You'll need a lot of determination for this chapter. But you'll be 'the one' after you're done.

How do you find the determinant of a 3D Matrix?

How do you find the area of an image for a 2 x 2 matrix?

What is true for an object’s orientation, given the values of the determinant?

How do you find the volume of a 3 x 3 matrix?

How do you find the inverse of a 3D matrix?

For system of equations, describe geometrically what is the case when a set of three plane intersect, given a number of solutions?

What condition is required for a matrix and a transformation matrix to only have one solution?

Define Eigenvalues and Eigenvectors.

A is a transformation matrix, x is a 2 x 1 matrix:

( a )

( b )

How do you find the characteristic equation and what does this help achieve?

A is the transformation matrix, lambda is the eigenvalue, 𝐈 is the identity matrix.

State the Cayley-Hamilton Theorem.

What makes a square matrix a diagonal matrix?

How do you diagonalize a matrix?

How do you raise a matrix by a power?