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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
If in the determinant $\Delta = \left| {\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}} \right|$, ${A_1},{B_1},{C_1}$ $etc$. be the co-factors of ${a_1},{b_1},{c_1}$etc., then which of the following relations is incorrect
  • A
    ${a_1}{A_1} + {b_1}{B_1} + {c_1}{C_1} = \Delta $
  • B
    ${a_2}{A_2} + {b_2}{B_2} + {c_2}{C_2} = \Delta $
  • C
    ${a_3}{A_3} + {b_3}{B_3} + {c_3}{C_3} = \Delta $
  • ✓
    ${a_1}{A_2} + {b_1}{B_2} + {c_1}{C_2} = \Delta $
✓

Answer

Correct option: D.
${a_1}{A_2} + {b_1}{B_2} + {c_1}{C_2} = \Delta $
d
(d) It is a fundamental concept.

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