🔢 Topic Summary
Matrix addition and subtraction are fundamental operations in linear algebra. To add or subtract matrices, they must have the same dimensions (i.e., the same number of rows and columns). The resulting matrix is obtained by adding or subtracting the corresponding elements of the original matrices.
For example, if $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ and $B = \begin{bmatrix} e & f \\ g & h \end{bmatrix}$, then $A + B = \begin{bmatrix} a+e & b+f \\ c+g & d+h \end{bmatrix}$ and $A - B = \begin{bmatrix} a-e & b-f \\ c-g & d-h \end{bmatrix}$.
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Matrix |
A. The result of adding or subtracting two matrices. |
| 2. Dimensions |
B. A rectangular array of numbers, symbols, or expressions arranged in rows and columns. |
| 3. Element |
C. The size of a matrix, defined by the number of rows and columns. |
| 4. Addition/Subtraction |
D. A single item in a matrix. |
| 5. Resultant Matrix |
E. The operation performed on matrices of the same dimensions. |
✍️ Part B: Fill in the Blanks
Matrices can only be added or subtracted if they have the same __________. When adding or subtracting matrices, you perform the operation on the corresponding __________. The resulting matrix will have the same __________ as the original matrices. Matrix addition is __________, meaning the order in which you add the matrices does not matter. The __________ element in the resultant matrix is the sum or difference of the corresponding elements in the original matrices.
🤔 Part C: Critical Thinking
Explain in your own words why it's important for matrices to have the same dimensions before you can add or subtract them. What would happen if you tried to add two matrices with different dimensions?