pre-calc unit 4C - Matrices

Matrix definition

A rectangular array of real #, defined by m rows x n columns (mxn)

Square matrix

A matrix where the # of rows is equal to the # of columns

Row matrix

Matrix w/ only one row

Column matrix

Matrix w only one column

Equal matrices

When 2 matrices are equal & have the same dimensions

Matrix addition & subtraction

Can only add/subtract if both matrices are the same dimension, then add corresponding elements

What is the sum of two matrices of different dimensions

Undefined

Scalar multiplication

Multiply each element of a matrix by c

Zero matrix property

Matrix equivalent/consist of the number zero

Commutative property

Associative property

Scalar identity

Additive identity

Distributive property

Matrix multiplication rules

Determinant definition

Determinant of a matrix is a scalar representation of the matrix

Determinant of a 2×2 matrix

Area of a parallelogram

Can find by putting the 2 vectors in a 2×2 matrix & finding the determinant

Identity matrix

A square matrix with 1s on the diagonal and 0s everywhere else

Hor to find identity matrix

The product of a matrix & its inverse

Invertible definition

A matrix with an inverse

Singular definition

A matrix that does not have an inverse

Inverse formula of a 2×2 matrix

Reflection over y =x

Reflection over x-axis

Reflection over y-axis

Horizontal dilation

Vertical dilation

Entire figure dilation

90° counterclockwise rotation about the origin

180° counterclockwise rotation about origin

270° counterclockwise rotation about origin

360° counterclockwise rotation about origin

Rotate counterclockwise by an angle of theta

Linear transformation

Inverse linear transformation