Find the Inverse [[30,36,42],[66,81,96],[102,126,150]]

Problem

[[30,36,42],[66,81,96],[102,126,150]]

Solution

1. Identify the matrix A and its dimensions.

A=[[30,36,42],[66,81,96],[102,126,150]]

2. Calculate the determinant of the matrix using the cofactor expansion along the first row.

det(A)=30*(81⋅150−96⋅126)−36*(66⋅150−96⋅102)+42*(66⋅126−81⋅102)

3. Simplify the products within the determinant calculation.

81⋅150=12150

96⋅126=12096

66⋅150=9900

96⋅102=9792

66⋅126=8316

81⋅102=8262

4. Substitute the products back into the determinant expression.

det(A)=30*(12150−12096)−36*(9900−9792)+42*(8316−8262)

5. Perform the subtractions.

det(A)=30*(54)−36*(108)+42*(54)

6. Finalize the determinant value.

30⋅54=1620

36⋅108=3888

42⋅54=2268

det(A)=1620−3888+2268

det(A)=0

7. Conclude based on the determinant. Since the determinant is zero, the matrix is singular and does not have an inverse.

Final Answer

[[30,36,42],[66,81,96],[102,126,150]](−1)=Undefined (Singular Matrix)

Want more problems? Check here!