Matrix Addition
Matrices of equal size add entry by entry.
Formula
Variables
Example
[[1,2],[3,4]] + [[5,6],[7,8]] = [[6,8],[10,12]].
How it works
Matrix addition is defined by matching positions: the entry in row i, column j of the sum is found by adding the two entries in that same position. This works only when the matrices have the same dimensions, because there must be a one-to-one pair of entries to combine. The rule preserves the structure of the data, so you can add two grids of numbers without mixing rows or columns.
When to use it
Use matrix addition when combining two data sets with the same layout, such as two tables of measurements, two images represented as pixel grids, or two linear transformations written as matrices. It is also common in systems where separate effects are added together, like displacement vectors arranged in matrix form.
Worked example, step by step
Let A = [[2, -1, 4], [0, 3, 5]] and B = [[7, 6, 1], [-2, 8, -3]]. Add corresponding entries: (1,1): 2 + 7 = 9 (1,2): -1 + 6 = 5 (1,3): 4 + 1 = 5 (2,1): 0 + (-2) = -2 (2,2): 3 + 8 = 11 (2,3): 5 + (-3) = 2 So A + B = [[9, 5, 5], [-2, 11, 2]].
Common mistakes to avoid
- Trying to add matrices of different sizes
- Adding rows to rows or columns to columns instead of matching each entry position
- Forgetting that negative numbers and zero still follow the same addition rule
Did You Know?
Matrices add entry by entry, but only if they're exactly the same shape.
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