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Multiplying Matrices

Multiplying Matrices. With an immediate use for it. Vocabulary. Identity Matrix: a diagonal matrix with 1 for every entry along the diagonal. Any time you multiply an identity matrix times another matrix, or another matrix times an identity matrix, you get the other matrix.

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Multiplying Matrices

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  1. Multiplying Matrices With an immediate use for it

  2. Vocabulary • Identity Matrix: a diagonal matrix with 1 for every entry along the diagonal. Any time you multiply an identity matrix times another matrix, or another matrix times an identity matrix, you get the other matrix. • Inverse matrix: any time you multiply a matrix by its inverse you get the identity matrix.

  3. A little notation • Matrices are usually named by a capital letter. For instance, matrix A. • Scalar multiplication of a matrix can be implied just like in a normal expression. For instance, 4A means 4 times matrix A. • Other operations can also be implied just like they were normal variables. E.g., 2A + 3B or 4A*B • To identify a specific entry in a matrix, use subscripts Arc. E.G. A12 would be matrix A, row 1, column 2.

  4. How to Multiply Matrices **Remember, the number of columns in the first matrix must equal the number of rows in the second matrix.** Multiply the first row of the first matrix by the first column of the second matrix. Add the results together. Put your answer in the first row, first column of the answer matrix. Repeat this for every possible combination of rows and columns.

  5. Actually… It’s easier to see it.

  6. Dealing with Data • Whenever you put points into a matrix, you always put the x coordinates in the first row and the y coordinates in the second row. Usually, you list the points in the same order they are given to you. • If you multiply two data matrices together, then the rows of the answer matrix will have the same meaning as the rows of the first matrix, and the columns of the answer matrix will have the same meaning as the columns of the second matrix.

  7. Geometric Transformations • Any polygon can be represented with a 2xn matrix, where n is the number of sides in the polygon. • There is a set of seven special 2x2 matrices that, when multiplied to the 2xn polygon matrix, will transform the polygon in the coordinate plane. • You can either memorize these 7, or you can learn to figure out which is which on the fly.

  8. The Seven Identity Reflect y-axis Reflect x-axis Reflect Origin Reflect y=x Rotate 270° Rotate 90° Rotate 180°

  9. Let’s See it!

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