Find the Inverse det [[x,7],[6,2]]=-44

Problem

det(x)=−44

Solution

1. Apply the determinant formula for a 2×2 matrix, which is a*d−b*c

x(2)−(7)*(6)=−44

2. Simplify the expression on the left side of the equation.

2*x−42=−44

3. Isolate the variable term by adding 42 to both sides of the equation.

2*x=−44+42

2*x=−2

4. Solve for x by dividing both sides by 2

x=(−2)/2

x=−1

5. Identify the matrix A using the value of x

A=[[−1,7],[6,2]]

6. Apply the inverse formula for a 2×2 matrix A=[[a,b],[c,d]] which is A(−1)=1/det(A)*[[d,−b],[−c,a]]

A(−1)=1/(−44)*[[2,−7],[−6,−1]]

7. Distribute the scalar to each element inside the matrix.

A(−1)=[[2/(−44),(−7)/(−44)],[(−6)/(−44),(−1)/(−44)]]

8. Simplify the fractions to find the final inverse matrix.

A(−1)=[[−1/22,7/44],[3/22,1/44]]

Final Answer

[[−1,7],[6,2]](−1)=[[−1/22,7/44],[3/22,1/44]]

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