Find the Inverse [[a,0,0],[0,b,0],[0,0,c]]

Problem

[[a,0,0],[0,b,0],[0,0,c]]

Solution

1. Identify the matrix type as a diagonal matrix, where all entries outside the main diagonal are zero.

2. Recall the property that the inverse of a diagonal matrix is found by taking the reciprocal of each entry on the main diagonal.

3. Assume that the matrix is invertible, which requires that the determinant is non-zero, meaning a≠0 b≠0 and c≠0

4. Calculate the reciprocal for each diagonal element: a⇒1/a b⇒1/b and c⇒1/c

5. Construct the inverse matrix using these reciprocal values on the main diagonal.

Final Answer

[[a,0,0],[0,b,0],[0,0,c]](−1)=[[1/a,0,0],[0,1/b,0],[0,0,1/c]]

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