All About Matrices

Any rectangular array of numbers in rows and columns, usually surrounded by square brackets. The size or dimension is important. The contents of the matrix are called its elements. What is a Matrix? Brackets

Properties of Matrices The number of rows is always reported before the number of columns. Rows go across Columns go up and down Dimension: This is a 3 x 2 matrix Because you have 3 rows and 2 columns [ ] 2 4 6 9 5 3 Element (1,2) = 4 Element(3,2) = 3

This matrice has 2 rows and 3 columns. The dimension of this matrice is (2 x 3)

Give the dimensions of the following matrices Examples Give the dimensions of the following matrices 1.) 2.)

Examples [ ] [ ] [ ] -4 12 6 12 –3 8 4 3 4 8 8 4 5 6 2 3 4 4 4 6

Examples Construct a (2 x 4) matrice that has an element at (2, 3) = 0 1.) Construct a (2 x 4) matrice that has an element at (2, 3) = 0   2.) Construct a (2 x 1) matrice that has an element at (2, 1) = -3

Examples 1.) 2.)

Discover the Math – page 52 Thomas’s Report for November Sales white black S T T = T-shirts S = sweatshirts What does element (1,1) represent? Row 1, Column 1 What does element (2,2) represent? Row 2, Column 2

Discover the Math – page 52 Thomas’s Report for December Sales white black s t T = T-shirts S = sweatshirts What does element (1,1) represent? What does element (2,2) represent?

Discover the Math – page 52 Thomas’s Report for Nov/Dec Sales white black s t T = T-shirts S = sweatshirts Dimensions are (2 x 2)

Discover the Math – page 52 Thomas’s Report for November Sales white black s t T = T-shirts S = sweatshirts What does element (1,1) represent? What does element (2,2) represent?

Adding & Subtracting Matrices You can only add two matrices if they have the same dimension. + = =

Adding & Subtracting Matrices = +

+ = YOU CANNOT ADD/SUBTRACT MATRICES WITH DIFFERENT DIMENSIONS. Not Possible + = (2 x 3) (3 x 1)

(Scalar) x (Matrice) 3 x = 2 x =

Assignment Page 56 Communicate the Key Ideas 1, 3, 4