Problem 57 - College Algebra

Question

Describe matrices that cannot be added or subtracted.

Step-by-Step Solution

Answer

Matrices that cannot be added or subtracted are those that do not have the same number of rows and columns.

Step 1: Understanding Matrix Operations

Matrix addition and subtraction are two of the simplest operations concerning matrices. Each entry in the spaces of these matrices are added or subtracted respectively. However, matrix addition and subtraction can only be performed on matrices of the exact same dimensions, meaning that the matrices must have the same number of rows and the same number of columns.

Step 2: Defining Incompatible Dimensions

If two matrices have different dimensions, they cannot be added or subtracted. In other words, if one matrix is of dimensions \(m \times n\) where \(m\) is the number of rows and \(n\) is the number of columns, and the other matrix is of dimensions \(p \times q\), they can only be added or subtracted if \(m = p\) and \(n = q\). If these conditions are not met, the matrices are not compatible for addition or subtraction.

Step 3: Conclusion

Hence, the matrices that cannot be added or subtracted are those matrices with incompatible dimensions. Precisely, if two matrices do not have the same number of rows and the same number of columns, then they cannot be added or subtracted according to the rules of matrix operations.