Question and Answers Forum

All Questions      Topic List

UNKNOWN Questions

Previous in All Question      Next in All Question      

Previous in UNKNOWN      Next in UNKNOWN      

Question Number 55846 by gunawan last updated on 05/Mar/19

$$\mathrm{If}x,y,z\mathrm{are}\mathrm{in}\mathrm{AP}.\mathrm{Then}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{the}$$$$\mathrm{determinant}$$$$\left|\begin{array}{ccc}a+2& a+3& a+2x\\ a+3& a+4& a+2y\\ a+4& a+5& a+2z\end{array}\right|\mathrm{is}$$

Answered by math1967 last updated on 05/Mar/19

$$\left|\begin{array}{ccc}\mathrm{a}+2& \mathrm{a}+3& \mathrm{a}+2\mathrm{x}\\ \mathrm{a}+3-\mathrm{a}-2& \mathrm{a}+4-\mathrm{a}-3& \mathrm{a}+2\mathrm{y}-\mathrm{a}-2\mathrm{x}\\ \mathrm{a}+4-\mathrm{a}-3& \mathrm{a}+5-\mathrm{a}-4& \mathrm{a}+2\mathrm{z}-\mathrm{a}-2\mathrm{y}\end{array}\right|{\mathrm{R}}_2^{{}^{\prime }}\to {\mathrm{R}}_2-{\mathrm{R}}_1,{\mathrm{R}}_3^{{}^{\prime }}\to {\mathrm{R}}_3-{\mathrm{R}}_2$$$$\left|\begin{array}{ccc}\mathrm{a}+2& \mathrm{a}+3& \mathrm{a}+2\mathrm{x}\\ 1& 1& 2(\mathrm{y}-\mathrm{x})\\ 1& 1& 2(\mathrm{z}-\mathrm{y})\end{array}\right|$$$$\left|\begin{array}{ccc}\mathrm{a}+2& \mathrm{a}+3& \mathrm{a}+2\mathrm{x}\\ 1& 1& 2(\mathrm{y}-\mathrm{x})\\ 1& 1& 2(\mathrm{y}-\mathrm{x})\end{array}\right|\because \mathrm{x},\mathrm{y},\mathrm{z}\mathrm{are}\mathrm{inA}.\mathrm{P}\therefore \mathrm{y}-\mathrm{x}=\mathrm{z}-\mathrm{y}$$$$=0\mathrm{ans}\left[{\mathrm{R}}_2\mathrm{and}{\mathrm{R}}_3\mathrm{identical}\right]$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com