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Question
Using properties of determinants, prove that
`|[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]|=2|[a,b,c],[p,q,r],[x,y,z]|`
Solution
Operating C1→ C1-(C+ C3 ), we get
LHS= `|[-2a,c+a,a+b],[-2p,r+p,q+p],[-2x,z+z,x+y]|`
`=-2|[a,c+a,a+b],[p,r+p,p+q],[x,z+x,x+y]|`
C2→C2-C1 and C3→C3-C1 ⇒`LHS=-2|[a,c,b],[p,r,q],[x,z,y]|`
C2↔C3= `2|[a,b,c],[p,q,r],[x,y,z]|=RHS`
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