Perform addition, subtraction, and multiplication of matrices, and understand their basic properties.
Matrices of the same order (dimensions) can be added or subtracted by combining corresponding elements.
Add [[1,2],[3,4]] and [[5,6],[7,8]].
[[6,8],[10,12]]
Subtract [[5,3],[2,1]] from [[8,7],[6,5]].
[[3,4],[4,4]]
Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second. Each entry is a sum of products.
Multiply [[1,2]] (1×2) by [[3],[4]] (2×1).
[1×3+2×4]=[11]
Multiply [[1,0],[0,1]] by [[5,6],[7,8]].
The identity matrix leaves the other matrix unchanged: [[5,6],[7,8]]
1. Add [[2,1],[0,3]] and [[1,4],[2,1]].
2. Subtract [[1,1],[1,1]] from [[4,3],[2,5]].
3. Multiply [[2,3]] by [[1],[2]].
4. Multiply [[1,2],[3,4]] by [[2,0],[1,2]].
5. What condition must two matrices satisfy to be added together?