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Maths-

General

Easy

Question

Consider the matrix A, B, C, D with order 2 × 3, 3×4, 4×4, 4×2 respectively. Let x = ( $alpha$ A B $gamma$ C² D)³ where $alpha$ & $gamma$ are scalars . Let |x| = k|ABC²D|³, then k is

$α$ $γ$
$α^{2} γ^{2}$
$α^{4} γ^{4}$
$α^{6} γ^{6}$

The correct answer is: $alpha to the power of 6 gamma to the power of 6$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals open parentheses alpha gamma A B C squared D close parentheses cubed end cell row cell vertical line x vertical line equals open vertical bar alpha gamma A B C squared D close vertical bar cubed end cell row cell text order of end text A B C squared D text is end text 2 cross times 2 end cell row cell vertical line x vertical line equals open parentheses alpha squared gamma squared close parentheses cubed open vertical bar A B C squared D close vertical bar cubed end cell row cell therefore k equals alpha to the power of 6 gamma to the power of 6 end cell end table$

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