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Unformatted text preview: Matrix Operations © Arizona State University, Department of Mathematics and Statistics 1 of 4 Objectives: At the end of this lesson, you should be able to: 1. Define the matrix operations. 2. Apply the matrix operations. 3. Create a matrix equation. Background Matrices create a mathematical structure that has many properties similar to the real numbers system. They also have some distinctly different properties. The differences are where the fun comes in. Think back on the real number system. We can add, subtract, multiply and applies powers and apply a multiplicative inverse to create results the real number system. We can do the same thing with matrices as long as we obey some simple rules. Most of the rules require us to pay attention to the size of the matrix . Addition and Subtraction We can add or subtract matrices of exactly the same size . We do this by combining the elements within the matrix in the same ( corresponding ) position. Let’s name our matrices A and B where and . 11 1 1 n m mn a a A a a = … v d v m 11 1 1 n m mn b b B b b = … v d v m Then . 11 11 1 1 1 1 n n m m mn mn a b a b A B a b a b ± ± ± = ± ± … v d v m Notice that this requires the matrices to both be m×n. If they are not, the sum is not defined. Examples: The two matrices are both 2×2, so we add element by element. These two matrices are different sizes (2×2 and 2×3). We cannot add them. This is undefined . These two matrices are different sizes (3×2 and 2×3). We cannot add them. This is also undefined . 1 3 10 1 10 3 0 9 3 2 1 11 2 1 11 2 12-- + + + = = + + 1 3 10 4 2 1 5 11- + 1 3 10 4 4 5 5 11 2 1- + Matrix Operations © Arizona State University, Department of Mathematics and Statistics 2 of 4 The two matrices are interesting! They create a field of zeroes in theThe two matrices are interesting!...
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