Matrices can be added or subtracted if they have the same dimensions.
The product of two matrices is only defined if the number of columns in the first matrix equals the number of rows in the second matrix.
The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.
The inverse of a matrix exists only if the matrix is square and its determinant is non-zero.
Gaussian elimination involves using row operations to transform a matrix into its reduced row echelon form to solve systems of linear equations.
Review Questions
What are the conditions for adding two matrices?
How do you determine if a matrix has an inverse?
What is the purpose of Gaussian elimination?
Related terms
Determinant: A scalar value that can be computed from the elements of a square matrix, which determines whether a matrix has an inverse.
Identity Matrix: A square matrix with ones on the diagonal and zeros elsewhere, denoted as $I$.
Reduced Row Echelon Form: A form of a matrix where each leading entry is one, and all entries in the column above and below each leading one are zeros.