શ્રેણિક left[ {begin{array}{*{20}{c}}2&lambda &{ - 4}{ - 1}&3&41&{ - 2}&{ - 3}end{array}} right] એ સામાન્ય શ્રેણિક હોય હોય તો ..... .

Q: શ્રેણિક $\left[ {\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}} \right]$ એ સામાન્ય શ્રેણિક હોય હોય તો $ ..... .$

The given matrix $A = \left[ {\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}} \right]$ is non singular, if $|A|\, \ne 0$ $|A|\,\, = \left| {\,\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}\,} \right|\,$ $=\left| {\,\begin{array}{*{20}{c}}1&{\lambda + 3}&0\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}\,} \right|\,$,$[{R_1} \to {R_2} + {R_1}]$ $= \left| {\,\begin{array}{*{20}{c}}1&{\lambda + 3}&0\\0&1&1\\0&{ - \lambda - 5}&{ - 3}\end{array}\,} \right|$ $\left[ {\begin{array}{*{20}{c}}{{R_2} \to {R_2} + {R_3}}\\{{R_3} \to {R_3} - {R_1}}\end{array}} \right]$ $= 1\,( - 3 + \lambda + 5) \ne 0$ $ \Rightarrow \lambda + 2 \ne 0$ $ \Rightarrow \lambda \,\, \ne - 2.$

MCQ

ગુજરાતી માધ્યમ

શ્રેણિક $\left[ {\begin{array}{*{20}{c}}2&\lambda &{ - 4}\\{ - 1}&3&4\\1&{ - 2}&{ - 3}\end{array}} \right]$ એ સામાન્ય શ્રેણિક હોય હોય તો $ ..... .$

A$\lambda \ne - 2$
B$\lambda \ne 2$
C$\lambda \ne 3$
D$\lambda \ne - 3$

Easy

ધોરણ 12 સાયન્સ
ગણિત
3 and 4 . determinant and metrices
JEE

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