Find the Determinant [[2,4,8],[16,3,64],[128,256,512]]

Problem

det(2)

Solution

1. Factor out common terms from the rows to simplify the calculation. Factor 2 from the first row, 1 from the second row, and 128 from the third row.

det(A)=(2)*(1)*(128)*det(1)

2. Identify identical rows within the simplified matrix. The first row [1,2,4] is identical to the third row [1,2,4]

3. Apply the property of determinants which states that if a matrix has two identical rows, its determinant is zero.

det(1)=0

4. Calculate the final product by multiplying the factored constants by the determinant of the simplified matrix.

det(A)=256×0=0

Final Answer

det(2)=0

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