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 sameā€”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.


a set of numbers aligned vertically in a matrix
an element, coefficient, or constant in a matrix
a rectangular array of numbers
a set of numbers aligned horizontally in a matrix
scalar multiple
an entry of a matrix that has been multiplied by a scalar