Question and Answers Forum

All Questions      Topic List

Matrices and Determinants Questions

Previous in All Question      Next in All Question      

Previous in Matrices and Determinants      Next in Matrices and Determinants      

Question Number 9285 by suci last updated on 28/Nov/16

$$findthedeterminantofthematrixbelow$$$$\left[\begin{array}{cccc}1& 4& -3& 1\\ 2& 0& 6& 3\\ 4& -1& 2& 5\\ 1& 0& -2& 4\end{array}\right]$$

Answered by mrW last updated on 28/Nov/16

$$\mid \mathrm{A}\mid =\left|\begin{array}{cccc}1& 4& -3& 1\\ 2& 0& 6& 3\\ 4& -1& 2& 5\\ 1& 0& -2& 4\end{array}\right|$$$$\mathrm{R}4-\mathrm{R}1\mathrm{and}\mathrm{R}3-\mathrm{R}2\times 2:$$$$\mid \mathrm{A}\mid =\left|\begin{array}{cccc}1& 4& -3& 1\\ 2& 0& 6& 3\\ 0& -1& -10& -1\\ 0& -4& 1& 3\end{array}\right|$$$$\mathrm{R}2-\mathrm{R}1\times 2:$$$$\mid \mathrm{A}\mid =\left|\begin{array}{cccc}1& 4& -3& 1\\ 0& -8& 12& 1\\ 0& -1& -10& -1\\ 0& -4& 1& 3\end{array}\right|$$$$=1\times \left|\begin{array}{ccc}-8& 12& 1\\ -1& -10& -1\\ -4& 1& 3\end{array}\right|$$$$\mathrm{R}2+\mathrm{R}1:$$$$=1\times \left|\begin{array}{ccc}-8& 12& 1\\ -9& 2& 0\\ -4& 1& 3\end{array}\right|$$$$\mathrm{R}3-\mathrm{R}1\times 3:$$$$=1\times \left|\begin{array}{ccc}-8& 12& 1\\ -9& 2& 0\\ 20& -35& 0\end{array}\right|$$$$=1\times 1\times \left|\begin{array}{cc}-9& 2\\ 20& -35\end{array}\right|$$$$=(-9)\times (-35)-2\times 20=275$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com