Section 6.2 Operations With Matrices
Matrix arithmetic extends familiar operations like addition and multiplication to the world of matrices. We’ll learn how to add, subtract, and multiply matrices, explore properties of these operations, and see how they’re used to solve systems of equations, represent compositions of transformations, and work with data in structured ways.
Subsection 6.2.1 Matrix Arithmetic
Matrices can be added, subtracted, and multiplied. However, unlike matrix multiplication, the addition and subtraction of matrices are performed element-wise. The identity matrix serves as the multiplicative identity for matrices, and the zero matrix serves as the additive identity.
Multiplication with matrices comes in several forms. Scalar multiplication scales every entry in a matrix by a constant. Matrix-vector multiplication treats the vector as a column and combines it with the matrix using dot products. Matrix-matrix multiplication is only defined when the number of columns in the first matrix matches the number of rows in the second, and is performed by computing dot products of rows and columns.
Note that to use the result of these operations, you would need to assign them to a variable.
