If A=⎡⎢⎣3−342−340−11⎤⎥⎦ then find Adj(AdjA).
A
⎡⎢⎣3−342−340−11⎤⎥⎦
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B
⎡⎢⎣3342−3−40−11⎤⎥⎦
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C
⎡⎢⎣3342−34011⎤⎥⎦
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D
⎡⎢⎣3−342−3−4011⎤⎥⎦
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Solution
The correct option is A⎡⎢⎣3−342−340−11⎤⎥⎦ We know that Adj(AdjA)=|A|n−2A Since A=⎡⎢⎣3−342−340−11⎤⎥⎦ Here n=3 (3 order matrix) ∴|A|=∣∣
∣∣3−342−340−11∣∣
∣∣ =3(1)+3(2−0)+4(−2−0) =1≠0,∴A is non-singular. ∴Adj(AdjA)=|A|3−2.A=|A|.A=1.A=A=⎡⎢⎣3−342−340−11⎤⎥⎦