Final answer:
To show a matrix is not invertible, the determinant must be zero. For a 2x2 matrix, if the equation \(ad - bc = 0\) holds, it's not invertible. Without specific entries, we cannot determine non-invertibility unless the matrix has certain properties leading to a determinant of zero.
Step-by-step explanation:
To show that a matrix is not invertible, we typically demonstrate that its determinant is zero. A nonzero determinant suggests that the matrix is invertible, whereas a determinant of zero means that the matrix is singular (not invertible), as it does not have a unique solution or inverse. For example, if the matrix in question is a 2x2 matrix represented as:
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]
Then the determinant of this matrix is calculated as \(ad - bc\). If \(ad - bc = 0\), the matrix is not invertible for any values of \(a\), \(b\), \(c\), and \(d\) that make this equation true. Therefore, to prove non-invertibility, we need to find a condition or a set of conditions upon the entries that will always make the determinant zero.
Without knowledge of the specific entries of the matrix, the question cannot be definitively answered. However, if the matrix has properties like two proportional rows or columns or has a row or column of zeros, then it would always be non-invertible regardless of the other entries.