Question

If $[5\overline{a}+2\overline{b},4\overline{c},\overline{d}]=\lambda \left[\overline{a}\overline{c}\overline{d}\right]+\mu \left[\overline{b}\overline{c}\overline{d}\right]$ then $\lambda +\mu =$

• A. 18
• B. 20
• C. 28
• D. None of these

Answer 1

Answer: (C)

28

$[5\overline{a}+2\overline{b},4\overline{c},\overline{d}]=[5\overline{a},4\overline{c},\overline{d}]+[2\overline{b},4\overline{c},\overline{d}]$
$=5\times 4[\overline{a},\overline{c},\overline{d}]+4\times 2[\overline{b},\overline{c},\overline{d}]=20\left[\overline{a}\overline{c}\overline{d}\right]+8\left[\overline{b}\overline{c}\overline{d}\right]=\lambda \left[\overline{a}\overline{c}\overline{d}\right]+\mu \left[\overline{b}\overline{c}\overline{d}\right]$
Hence $\lambda +\mu =28$