Subtract Matrices

Subtracting Matrices

Matrix subtraction is done entry by entry. You can only subtract matrices of the same size, meaning they must have the same number of rows and columns.

Method

1. Check the dimensions of both matrices.
   • If they do not match, subtraction is not defined.
2. Subtract matching entries.
   • Subtract the element in row 1, column 1 of the second matrix from the corresponding element in the first matrix.
   • Continue in the same position for every entry.
3. Write the result in matrix form.

Example pattern

If [ A=\begin{bmatrix}a&b\c&d\end{bmatrix}, \quad B=\begin{bmatrix}e&f\g&h\end{bmatrix}, ] then [ A-B=\begin{bmatrix}a-e&b-f\c-g&d-h\end{bmatrix}. ]

Common mistakes

• Subtracting rows or columns as whole objects instead of matching entries.
• Forgetting that the second matrix is subtracted from the first.
• Mixing up positions in larger matrices.

Quick check

After finding your answer, compare each position separately: first entry minus first entry, second minus second, and so on. If possible, add your result to the matrix you subtracted and see whether you get back the original first matrix.