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 sameāthe 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
Candela Citations
CC licensed content, Original
- Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution
CC licensed content, Shared previously
- College Algebra. Authored by: Abramson, Jay et al.. Provided by: OpenStax. Located at: http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@5.2. License: CC BY: Attribution. License Terms: Download for free at http://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@5.2
CC licensed content, Specific attribution
- Precalculus. Authored by: OpenStax College. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution