Matrix Determinant Properties Example #3 - Linear Algebra Example Problems

Consider the square matrices A and B, where B is the same as A except one row has been been replaced with a linear combination of rows from A. In this case, we have that det(A) = det(B). In general, replacing a row of a matrix with a linear combination of other rows does not change the value of the matrix determinant.

This video does not prove this result, but demonstrates the property with a simple example.