For a 3×33 \times 33×3 matrix AAA with eigenvalues λ1=2\lambda_1 = 2λ1=2, λ2=−1\lambda_2 = -1λ2=−1, and λ3=3\lambda_3 = 3λ3=3, what is det(A)\det(A)det(A)?
det(A)=2+(−1)+3=4\det(A) = 2 + (-1) + 3 = 4det(A)=2+(−1)+3=4
det(A)=2⋅(−1)⋅3=−6\det(A) = 2 \cdot (-1) \cdot 3 = -6det(A)=2⋅(−1)⋅3=−6
det(A)=∣2∣+∣−1∣+∣3∣=6\det(A) = |2| + |-1| + |3| = 6det(A)=∣2∣+∣−1∣+∣3∣=6
det(A)=22+(−1)2+32=14\det(A) = \sqrt{2^2 + (-1)^2 + 3^2} = \sqrt{14}det(A)=22+(−1)2+32=14