| , * 20 c bc & bc' + b'c & b'c' ca & ca' + c'a & c'a' ab & ab' +… - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}{bc}&{bc' + b'c}&{b'c'}\\{ca}&{ca' + c'a}&{c'a'}\\{ab}&{ab' + a'b}&{a'b'}\end{array}\,} \right|$ is equal to

A
$(ab - a'b')(bc - b'c')(ca - c'a')$
B
$(ab + a'b')(bc + b'c')(ca + c'a')$
✓
$(ab' - a'b)(bc' - b'c)(ca' - c'a)$
D
$(ab' + a'b)(bc' + b'c)(ca' + c'a)$

✓

Answer

Correct option: C.

$(ab' - a'b)(bc' - b'c)(ca' - c'a)$

c
(c) Trick : Put $a = 1,\,b = - 1,\,c = 0$

$a' = 2,\,b' = 2,\,c' = 1$

Then the determinant is $\left| {\,\begin{array}{*{20}{c}}0&{ - 1}&2\\0&1&2\\{ - 1}&0&4\end{array}\,} \right| = 4$

Option $ (c) $ also gives the same value.

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