For the diagonal matrix D=(5000−30002)D = \begin{pmatrix} 5 & 0 & 0 \\ 0 & -3 & 0 \\ 0 & 0 & 2 \end{pmatrix}D=5000−30002, what is det(D)\det(D)det(D)?
5+(−3)+2=45 + (-3) + 2 = 45+(−3)+2=4
5×(−3)×2=−305 \times (-3) \times 2 = -305×(−3)×2=−30
∣5×(−3)×2∣=30|5 \times (-3) \times 2| = 30∣5×(−3)×2∣=30
52+32+22=38\sqrt{5^2 + 3^2 + 2^2} = \sqrt{38}52+32+22=38