Find the Inverse [[30,50,65],[40,50,40],[50,50,15]]

Problem

[[30,50,65],[40,50,40],[50,50,15]](−1)

Solution

1. Calculate the determinant of the matrix A using the first row.

det(A)=30*(50⋅15−40⋅50)−50*(40⋅15−40⋅50)+65*(40⋅50−50⋅50)

det(A)=30*(750−2000)−50*(600−2000)+65*(2000−2500)

det(A)=30*(−1250)−50*(−1400)+65*(−500)

det(A)=−37500+70000−32500=0

2. Check for invertibility by observing the value of the determinant.

det(A)=0

3. Conclude that since the determinant is zero, the matrix is singular and does not have an inverse.

Final Answer

[[30,50,65],[40,50,40],[50,50,15]](−1)=Undefined (Matrix is singular)

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