Section 7-2 finding the inverse of a 2 x 2 matrix finding the inverse of a 3 x 3 matrix (calc.) properties of matrices applications that use matrices

Finding a 2 x 2 Inverse a square matrix will have an inverse unless its determinant is 0 use the following formula for a 2 x 2:

Finding a 3 x 3 Inverse  this will be done with a calculator (there is a non-calculator technique which we are not learning).  the matrix is entered into the calculator by pressing MATRIX then  to EDIT (change the order if necessary)  go back to the main screen and press MATRIX ENTER, then x -1, then ENTER

Properties of Matrices  even though the commutative property of multiplication does not work for matrices, there are still many algebraic properties that still hold true (like associative and distributive)  look over page 585 for a list of properties for matrices

Application – Reflecting Points matrices can be used to find “images” of points reflected over the x-axis and y-axis change the original point into a 1 x 2 matrix (i.e. (-2, 3) becomes [-2 3]) for x-axis, multiply it by for y-axis, multiply it by

Rotating a Point to rotate a point and find its image multiply it (as a 1 x 2 matrix) by the following matrix where θ is the amount of rotation