Mathegoras

Vectors and matrices › Determinants › Cofactor expansion

Determinant of a 4x4 matrix

High school · ●●○○○ 20 pts

Given ∣223xyza2b3c∣=10\begin{vmatrix} 2 & 2 & 3\\ x & y & z\\ a & 2b & 3c \end{vmatrix}=10 with x,y,z,a,b,c∈Rx,y,z,a,b,c \in \mathbb{R}, find ∣03xyz03a2b3c06235000∣\begin{vmatrix} 0 & 3x & y & z\\ 0 & 3a & 2b & 3c\\ 0 & 6 & 2 & 3\\ 5 & 0 & 0 & 0 \end{vmatrix}.

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