Adding and Subtracting Matrices

Definition: When two matrices have the same dimensions (number of rows and columns), they can be added or subtracted. If you want more information on matrices, click here.

To add/subtract matrices, you can add/subtract the corresponding elements.

Example: Add and subtract the following matrices:

Mat3.gif

Solution: 

Step 1: Check to ensure the matrices have the same dimensions. Matrix A has 2 rows and 3 columns, so its dimensions are 2×3 Matrix B has 2 rows and 3 columns, so its dimensions are also 2×3. This confirms that it is possible to add/subtract them.

Step 2: To add the given matrices, we can add each element in Matrix A with the corresponding element in Matrix B. For example, the element located at a₁₂ (1) will be added with the element at b₁₂ (1) to get a new value of 2. This value is then written at the same location in a new matrix:

Mat4.gif

Step 3: To subtract the given matrices, we can subtract each element in Matrix A with the corresponding element in Matrix B. For example, the element located at a₁₁ (1) will be subtracted with the element at b₁₁ (2) to get a new value of -1. This value is then written at the same location in a new matrix:

Mat5.gif

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