Find the Determinant

Problem

det(7)⋅4−3.085

Solution

1. Identify the matrix A for which the determinant must be calculated.

A=[[7,2.12,−3.25,5.2],[4,3,5,−2],[1.23,5.21,−4.03,7.2],[4.2,12.06,−3.085,4.74]]

2. Calculate the determinant of the 4×4 matrix using cofactor expansion or row reduction.

det(A)=7⋅det(3)−2.12⋅det(4)+…

3. Compute the numerical value of the determinant.

det(A)=113.1125

4. Multiply the resulting determinant by 4 as specified in the expression.

113.1125⋅4=452.45

5. Subtract 3.085 from the product to find the final value.

452.45−3.085=449.365

Final Answer

det(7)⋅4−3.085=449.365

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