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Evalute the determinants in queations 1 ...

Evalute the determinants in queations 1 and 2 : If `A=|{:(1,0,1),(0,1,2),(0,0,4):}|`

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`A=|{:(1,0,1),(0,1,2),(0,0,4):}|`
`rArr" "A=|{:(1,0,1),(0,1,2),(0,0,4):}|=1|{:(1,2),(0,4):}|-0-0=4-0=4`
`rArr" "27|A|=27xx4=108`
Now, `3A=|{:(3,0,3),(0,3,6),(0,0,12):}|`
`|3A|=|{:(3,0,3),(0,3,6),(0,0,12):}|=3|{:(3,6),(0,12):}|-0+0`
=3(36-0)108`
`therefore" "|A|=27|A|`
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Knowledge Check

  • If A= [(1,0,1),(0,1,2),(0,0,4)] ,then

    A
    |3A|=3|A|`
    B
    `|3A|=9|A|`
    C
    `|3A|=27|A|`
    D
    None of these

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    A
    `|A|=2`
    B
    A is non-singular
    C
    Adj. A=`=[{:(,1//2,-1//2,0),(,0,-1,1//2),(,0,0,-1//2):}]`
    D
    A is skew symmetric matrix

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