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Let A be any 3xx2 matrix. Then prove tha...

Let A be any `3xx2` matrix. Then prove that det. `(A A^(T))=0`.

Text Solution

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Let `A=[(a,p),(b,q),(c,r)]`
`:. A^(T)=[(a,b,c),(p,q,r)]`
`:. A A^(T)=[(a^(2)+p^(2),ab+pq,ac+pr),(ab+pq,b^(2)+q^(2),bc+qr),(ac+pr,bc+qr,c^(2)+r^(2))]`
det. `(A A^(T))=|(a,p,0),(b,q,0),(c,r,0)||(a,b,c),(p,q,r),(0,0,0)|=0`
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