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Determinants

Short Answer Type

1. Evaluates :

open vertical bar table row cell straight a plus ib end cell cell straight c plus id end cell row cell negative straight c plus ic end cell cell straight a minus ib end cell end table close vertical bar

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2. Evaluate

open vertical bar table row 2 cell space 4 end cell row cell negative 1 end cell cell space 2 end cell end table close vertical bar

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3. Evaluate

open vertical bar table row 2 cell space space space space space space 4 end cell row cell negative 5 end cell cell space space space minus 1 end cell end table close vertical bar

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4. Evaluate

open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar

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5. Evaluates :

open vertical bar table row cell 2 space cos space straight theta space space end cell cell negative 2 space sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close vertical bar

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6. Evaluate

left parenthesis straight i right parenthesis open square brackets table row cell cos space straight theta end cell cell negative sin space straight theta space end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close square brackets space left parenthesis ii right parenthesis space open square brackets table row cell straight x squared minus straight x plus 1 end cell cell straight x minus 1 end cell row cell straight x plus 1 end cell cell straight x plus 1 end cell end table close square brackets

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If A= $open square brackets table row 1 cell space space 2 end cell row 4 cell space space 2 end cell end table close square brackets comma space then space show space that space left enclose 2 space straight A space open vertical bar space equals 4 space close vertical bar space right enclose straight A space end enclose end enclose$

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8. Evaluates :

$open vertical bar table row cell sin space 30 degree end cell cell space space cos space 30 degree end cell row cell negative sin space 60 degree end cell cell space cos space 60 degree end cell end table close vertical bar$

Let space space increment space equals space open vertical bar table row cell sin space 30 degree end cell cell space space cos space 30 degree end cell row cell negative sin space 60 degree end cell cell space cos space 60 degree end cell end table close vertical bar space space space space space space space space space space space space equals space sin space 30 degree space cos space 60 degree space space plus space cos space 30 degree space space sin space 60 degree space equals space sin space left parenthesis 30 degree space plus 60 degree right parenthesis space space space space space space space space space space space space equals space sin space 90 degree space equals 1

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IF $open vertical bar table row straight x cell space space straight x end cell row 1 cell space space straight x end cell end table close vertical bar space equals space open vertical bar table row 3 cell space space space 4 end cell row 1 cell space space space 2 end cell end table close vertical bar$ , find the values of x.

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10. Find values of x for which

open vertical bar table row 3 cell space space space straight x end cell row straight x cell space space 1 end cell end table close vertical bar space equals space open vertical bar table row 3 cell space space 2 end cell row 4 cell space space 1 end cell end table close vertical bar

69 Views