Find the Determinant of the Resulting Matrix

Problem

det([[2,4],[8,1]]+[[−2,10],[3,5]]+[[5,20],[2,−21]])

Solution

1. Add the first two matrices by summing their corresponding entries.

[[2,4],[8,1]]+[[−2,10],[3,5]]=[[0,14],[11,6]]

2. Add the third matrix to the previous result to find the final matrix.

[[0,14],[11,6]]+[[5,20],[2,−21]]=[[5,34],[13,−15]]

3. Apply the determinant formula for a 2×2 matrix, which is det(a)=a*d−b*c

det(5)=(5)*(−15)−(34)*(13)

4. Calculate the products and subtract to find the final value.

(5)*(−15)=−75

(34)*(13)=442

−75−442=−517

Final Answer

det([[2,4],[8,1]]+[[−2,10],[3,5]]+[[5,20],[2,−21]])=−517

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