Week 2 Workshop - Vectors

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Matrices

$$S=\left(\begin{array}{ccc}-1& 2& 3\\ 2& -1& 4\\ 3& 4& 1\end{array}\right)$$ $$\det (S)=\det \left(\begin{array}{ccc}-1& 2& 3\\ 2& -1& 4\\ 3& 4& 1\end{array}\right)$$ $$-1\times \det \left(\begin{array}{cc}-1& 4\\ 4& 1\end{array}\right)-2\times \det \left(\begin{array}{cc}2& 4\\ 3& 1\end{array}\right)+3\times \det \left(\begin{array}{cc}2& -1\\ 3& 4\end{array}\right)$$ $$-1\times (-1-16)-2\times (2-12)+3\times (8-(-3))$$ $$17+20+33$$ $$=70$$ $$T=\left(\begin{array}{ccc}1& 2& 1\\ 2& 4& 6\\ 3& 1& 2\end{array}\right)$$ $$\det (T)=\det \left(\begin{array}{ccc}1& 2& 1\\ 2& 4& 6\\ 3& 1& 2\end{array}\right)$$ $$1\times \det \left(\begin{array}{cc}4& 6\\ 1& 2\end{array}\right)-2\times \det \left(\begin{array}{cc}2& 6\\ 3& 2\end{array}\right)+1\times \det \left(\begin{array}{cc}2& 4\\ 3& 1\end{array}\right)$$ $$1\times (8-6)-2\times (4-18)+1\times (2-12)$$ $$2+28-10$$ $$=20$$