Matrices on the ACT

ACT Math · Axiom Academy

A matrix is just a grid of numbers — the ACT tests four operations on it, and every one is mechanical if you go element by element. A matrix's size is always given as rows × columns . The matrix below has 2 rows and 3 columns, so it's called a "2 by 3" matrix. Every entry has an address: a_ ij means the entry in row i , column j . Dimensions: (rows) × (columns) a_ ij = the entry in row i , column j 2. Addition and Subtraction — Element by Element To add or subtract two matrices, they must have the exact same dimensions . Then you simply add (or subtract) the entries that sit in the same position — no cross-multiplying, no row/column rule. Watch each matching pair combine into the result. Each entry adds straight across: 1+3=4 , 2+4=6 , 5+7=12 , 6+8=14 . Subtraction works the same way, just subtracting instead of adding each pair. 3. Scalar Multiplication — Scale Every Entry A scalar is just an ordinary number (not a matrix). To multiply a matrix by a scalar, multiply every single entry by that number — no dimension restriction, and the result keeps the same dimensions as the original. Every entry gets multiplied by 2: 2(1)=2 , 2(2)=4 , 2(3)=6 , 2(4)=8 . 4. Matrix Multiplication — Row Meets Column Matrix multiplication is the one the ACT occasionally tests, and it's a different rule entirely: to find an entry in the product, take a row from the first matrix and a column from the second, multiply the matching pairs, and add them up.

This is the written version of the interactive lesson above. See the full ACT Math course.