Find the Inverse

Problem

[[0,0,0,1],[1,0,1,1],[1,1,1,1],[0,0,0,1]]

Solution

1. Check for invertibility by calculating the determinant of the matrix A

2. Observe the rows of the matrix. Notice that the first row (R_1)=[0,0,0,1] and the fourth row (R_4)=[0,0,0,1] are identical.

3. Apply the property of determinants which states that if a matrix has two identical rows, its determinant is zero.

4. Conclude that because det(A)=0 the matrix is singular.

5. Determine that a singular matrix does not have an inverse.

Final Answer

The matrix is singular and has no inverse.

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