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What is a matrix? How do you classify matrices? How do you identify elements of a matrix?

Matrix a matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers Example:

Elements of a Matrix individual entries of a matrix arranged in rows and columns Rows are first (right to left) Columns (up and down) Dimensions (size) Written by # of rows and # of columns Square matrix – when the # of rows and columns are the same (ex. 2x2) Rows are first (right to left) Columns (up and down) Dimensions (size) Written by # of rows and # of columns Square matrix – when the # of rows and columns are the same (ex. 2x2)

Naming elements A = Name a 23 B = Name b 23 A = Name a 23 B = Name b

warm up – please get started on this while I take attendance AIdentify the following 1. b22 B2. c13 3. a31 C4. Which one is a square matrix? 5. Find the dimensions of A,B, and C. AIdentify the following 1. b22 B2. c13 3. a31 C4. Which one is a square matrix? 5. Find the dimensions of A,B, and C

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Adding and Subtracting Matrices  Matrices must have the same dimensions in order to add or subtract them.  Add or subtract the elements that are in the same position (ex. A23 + B23)  When you subtract matrices, add the opposite (change the signs in the 2 nd matrix)  The resulting matrix will have the same dimensions.

Examples A+B2. A-B3. B-A

Scalar Multiplication ALL Multiply ALL elements A Find -2A

Now you try J K Find 3J – ½ K

Multiplying Matrices **Rule** The # of columns from the first matrix MUST match the # of rows from the second matrix The # of columns from the first matrix MUST match the # of rows from the second matrix Steps 1.Check your dimensions 2.Draw a blank template for the resulting matrix. 3.Multiply the first row from the first matrix times the first columns of the second 4.Add the products of each element 5.Multiply the first row from the first matrix times the second column of the second matrix 6.Add the products. 7.Continue the process Example A = B = AB =

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