To perform matrix subtraction, you subtract corresponding elements of two matrices, but only if they have the same dimensions. This means they must have the same number of rows and the same number of columns.
Here's a breakdown of the process:
Matrix Subtraction Explained
Matrix subtraction is a fundamental operation in linear algebra. The key is ensuring compatibility:
- Dimension Requirement: You can only subtract matrices of the same size (same number of rows and columns). According to the reference, "The subtraction of matrices or matrix subtraction can only be possible if the number of rows and columns of both the matrices are the same."
- Element-wise Subtraction: Subtract the corresponding elements in the matrices. The reference states, "While subtracting two matrices, we subtract the elements in each row and column from the corresponding elements in the row and column of the other matrix."
Steps for Matrix Subtraction
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Check Dimensions: Verify that both matrices have the same number of rows and columns. If they don't, subtraction is not possible.
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Subtract Corresponding Elements: Subtract the element in the first matrix from the corresponding element in the second matrix. This yields the corresponding element in the resulting matrix.
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Construct the Resultant Matrix: Place the results from Step 2 into a new matrix with the same dimensions as the original matrices.
Example
Let's say we have two matrices, A and B:
A = | 1 2 | B = | 5 6 |
| 3 4 | | 7 8 |To find A - B, we perform the following calculations:
- (1 - 5) = -4
- (2 - 6) = -4
- (3 - 7) = -4
- (4 - 8) = -4
Therefore, A - B is:
A - B = | -4 -4 |
| -4 -4 |Key Points to Remember
- Matrix subtraction is not commutative, meaning A - B is generally not the same as B - A.
- You can only subtract matrices of the same dimensions.
