Find the Inverse

Problem

[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]](−1)

Solution

1. Identify the matrix A and its dimensions.

A=[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]

2. Check for linear dependence between the rows of the matrix.

(R_2)−(R_1)=[[4,4,4,4]]

(R_3)−(R_2)=[[4,4,4,4]]

(R_4)−(R_3)=[[4,4,4,4]]

3. Observe that the rows follow an arithmetic progression, meaning the rows are linearly dependent.

(R_3)−(R_2)=(R_2)−(R_1)

(R_3)−2*(R_2)+(R_1)=0

4. Determine the determinant of the matrix. Since the rows are linearly dependent, the matrix is singular.

det(A)=0

5. Conclude that because the determinant is zero, the matrix does not have an inverse.

Final Answer

[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]](−1)=Does not exist (Singular Matrix)

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