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**4.1 Introduction to Matrices**

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About Matrices A matrix is a rectangular arrangement of numbers in rows and columns. Rows run horizontally and columns run vertically. The dimensions, or size, of a matrix are: # of rows X # of columns.

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Special Matrices Some matrices have special names because of what they look like. Row matrix: only has 1 row. Column matrix: only has 1 column. Square matrix: has the same number of rows and columns. Zero matrix: contains all zeros. Identity matrix: 1’s going down the main diagonal and zeros everywhere else

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**Dimensions: 4x1 COLUMN MATRIX Dimensions: 3x2**

Find the dimensions of each matrix. Dimensions: 4x1 COLUMN MATRIX Dimensions: 3x2 Dimensions: 2x4

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**Using Matrices to Solve Equations**

Equal Matrices - two matrices that have the same dimensions and each element of one matrix is equal to the corresponding element of the other matrix. *The definition of equal matrices can be used to find values when elements of the matrices are algebraic expressions.

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**Examples: Find the values for x and y**

* Since the matrices are equal, the corresponding elements are equal! Step 1: Form two linear equations. Step 2: Solve the system using any method.

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Plug y in to get x. Now check your answer:

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**Set each element equal and solve!**

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