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If A=[{:(1,-1,1),(0,2,-3),(2,1,0):}] and...

If `A=[{:(1,-1,1),(0,2,-3),(2,1,0):}]` and `B=(adjA)` and `C=5A`, then find the value of `(|adjB|)/(|C |)`

A

5

B

25

C

`-1`

D

1

Text Solution

Verified by Experts

`B = adj (A) = [{: ( 3,1,1), (-6,-2,3),(-4,-3,2):}]`, Therefore, `adj ( B) = [ {:(5,-5,5),(0,10,-15),(10,5,0):}]`
Now, `|adjB| = [{:(5,-5,5),(-6,-2,3),(10,5,0):}]=625` and `|C| = 125|A| = 125 [{:(1,-1,1),(0,2,-3),(2,5,0):}]=625`
`:. (|adj(B)|)/(|C|) = ( 625)/( 625) = 1 `
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