If a 4 by 4 matrix has deta=12, find det(2A),det(−A),det(A2), and det(A−1).

Evaluate using properties of determinants: det(2A)=24⋅detA=16⋅12=8 det(−A)=(−1)4⋅detA=1⋅12=12 det(A2)=detA⋅detA=12⋅12=14 det(A−1)=1detA=112=2 Result: 8,12,14,2

Answered: "If a 4 by 4 matrix has deta=12,"

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Fenian41

Answered question

2021-12-05

If a 4 by 4 matrix has $det a = \frac{1}{2}, f i n d det (2 A), det (- A), det (A^{2}), and det (A^{- 1})$ .

Answer & Explanation

Egreane61

Beginner2021-12-06Added 16 answers

Evaluate using properties of determinants:

det (2 A) = 2^{4} \cdot det A = 16 \cdot \frac{1}{2} = 8

det (- A) = {(- 1)}^{4} \cdot det A = 1 \cdot \frac{1}{2} = \frac{1}{2}

det (A^{2}) = det A \cdot det A = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

det (A^{- 1}) = \frac{1}{det A} = \frac{1}{\frac{1}{2}} = 2

Result:

8, \frac{1}{2}, \frac{1}{4}, 2

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