41006c17-e572-47d6-bcb0-df575291592f2bed8f86-056c-4137-9762-6a5d517c6efcbf9c8cfb-3123-438a-a941-8945554badac1.2.2.2<p>Invent a $$3\times3$$ matrix and compute its determinant.</p><p>$$B=\left(\begin{matrix} 3 & 1 & -1 \\ 0 & 1 & 2 \\ 1 & 1 & 0 \end{matrix} \right)$$</p> <p>$$det(B)=\left|\begin{matrix} 3 & 1 & -1 \\ 0 & 1 & 2 \\ 1 & 1 & 0 \end{matrix} \right|=3\cdot1\cdot0+0\cdot1\cdot(-1)+1\cdot1\cdot2-(-1)\cdot1\cdot1-2\cdot1\cdot3-0\cdot1\cdot0=$$</p> <p>$$=0+0+2+1-6-0=-3$$</p><p>$$det(B)=-3$$</p>7/18/16, 11:44 AM7/18/16, 11:44 AMec25674f-c94d-44b1-99a9-04edc9c745382bed8f86-056c-4137-9762-6a5d517c6efcbf9c8cfb-3123-438a-a941-8945554badac1.2.2.2<p>Compute the following determinants.</p> <p>$$\left|\begin{matrix} 1 & 0 & 0\\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}\right|$$, $$\left|\begin{matrix} 3 & 2 & 1\\ -2 & -1 & 0 \\ 2 & -5 & 0 \end{matrix}\right|$$</p><p>$$\left|\begin{matrix} 1 & 0 & 0\\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}\right| \rightarrow \begin{matrix} \left|\begin{matrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{matrix}\right| \\ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}\end{matrix}=1\cdot1\cdot1+0+0-0\cdot1\cdot0-0-0=1$$ </p> <p>$$\begin{matrix} \left|\begin{matrix} 3 & 2 & 1\\ -2 & -1 & 0\\ 2 & -5 & 0 \end{matrix}\right| \\ \begin{matrix} 3 & 2 & 1 \\ -2 & -1 & 0 \end{matrix}\end{matrix}=0+(-2)\cdot(-5)\cdot1+0-1\cdot(-1)\cdot2-0-0=12$$</p><p>$$1, 12$$</p>7/18/16, 11:44 AM7/18/16, 11:44 AM