Matrix Operations

Algebra 2 · Axiom Academy

Add and subtract matrices entry by entry, and scale every entry at once — sizes must match for . We describe a matrix by its dimensions , written rows × columns. Each number inside is an entry , addressed by its row and column position — so a 23 is the entry sitting in row 2, column 3. To add two matrices, add their corresponding entries . Because you pair entries up position by position, the two matrices have to be the same size . Subtraction works exactly like addition, but you subtract each pair of corresponding entries. The two matrices must still be the same size. A scalar is a single number. To multiply a matrix by a scalar k , multiply every entry by k . There's no size requirement — it works on any matrix. Addition and subtraction only make sense when every entry has a partner — so the two matrices must have identical dimensions . Line the shapes up: if they match, every position pairs off; if they don't, some entries are left stranded. Addition and subtraction need matching sizes; scalar multiplication works on any matrix. You've seen how matrices add, subtract, and scale — every operation happening one entry at a time. Scroll up to revisit any step.

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