# Summary: Matrices and Matrix Operations

## Key Concepts

- A matrix is a rectangular array of numbers. Entries are arranged in rows and columns.
- The dimensions of a matrix refer to the number of rows and the number of columns. A [latex]3\times 2[/latex] matrix has three rows and two columns.
- We add and subtract matrices of equal dimensions by adding and subtracting corresponding entries of each matrix.
- Scalar multiplication involves multiplying each entry in a matrix by a constant.
- Scalar multiplication is often required before addition or subtraction can occur.
- Multiplying matrices is possible when inner dimensions are the same—the number of columns in the first matrix must match the number of rows in the second.
- The product of two matrices, [latex]A[/latex] and [latex]B[/latex], is obtained by multiplying each entry in row 1 of [latex]A[/latex] by each entry in column 1 of [latex]B[/latex]; then multiply each entry of row 1 of [latex]A[/latex] by each entry in columns 2 of [latex]B,\text{}[/latex] and so on.
- Many real-world problems can often be solved using matrices.
- We can use a calculator to perform matrix operations after saving each matrix as a matrix variable.

## Glossary

**column**- a set of numbers aligned vertically in a matrix
**entry**- an element, coefficient, or constant in a matrix
**matrix**- a rectangular array of numbers

**row**- a set of numbers aligned horizontally in a matrix
**scalar multiple**- an entry of a matrix that has been multiplied by a scalar

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