19 Determine the condition number of the following matrices

19. Determine the condition number of the following matrices. Comment on whether or not small errors in data of each matrix A can result in 2 -3 (c) -2 (d) 61 li (b) (a)

Solution

When the determinant of a square matrix A is zero, A is not invertible. This is a crucial test that helps determine whether a square matrix is invertible, i.e. if the matrix has an inverse. When it does have an inverse, it allows us to find a unique solution.

When the determinant of a matrix is zero, the system of equations associated with it is linearly dependent, i.e, if the determinant of a matrix is zero, at least one row of such a matrix is a scalar multiple of another.

[When the determinant of a matrix is nonzero, linear system it represents is linearly independent]

When the determinant of a matrix is zero, it rows are linearly dependent vectors, and its columns are linearly dependent vectors.