what is the determinant of the coefficient matrix of the system $\begin{cases}-x - y+2z = 5\\3x + 2y - z =…
what is the determinant of the coefficient matrix of the system $\begin{cases}-x - y+2z = 5\\3x + 2y - z = 3\\4x + 4y - 8z=-2end{cases}$?\n0\n16\n18\n40
Answer
Explanation:
Step1: Write the coefficient matrix
The coefficient matrix $A$ of the system is $\begin{bmatrix}-1&-1&2\3&2&-1\4&4&-8\end{bmatrix}$.
Step2: Calculate the determinant
[ \begin{align*} \det(A)&=-1\times\begin{vmatrix}2&-1\4&-8\end{vmatrix}-(-1)\times\begin{vmatrix}3&-1\4&-8\end{vmatrix}+2\times\begin{vmatrix}3&2\4&4\end{vmatrix}\ &=-1\times(2\times(-8)-(-1)\times4)+1\times(3\times(-8)-(-1)\times4)+2\times(3\times4 - 2\times4)\ &=-1\times(-16 + 4)+1\times(-24 + 4)+2\times(12-8)\ &=-1\times(-12)+1\times(-20)+2\times4\ &=12-20 + 8\ &=0 \end{align*} ]
Answer:
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