Show that the matris `[[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]]` is orthogonal, `if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and` `l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).`A.B.C.D.

Show that the matris `[[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),

1.	Show that the matris `[[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]]` is orthogonal, `if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and` `l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).`A.B.C.D.
Answer» `Let A =[[l_(1) , m_(1), n_(1)],[l_(2), m_(2), n_(2) ],[l_(3),m_(3),n_(3)]]` `therefore A^(T) = [[l_(1),l_(2), 1_(3)],[m_(1) ,m_(2),m_(3) ],[n_(1),n_(2),n_(3)]]` Now, `A A^(T) =[[l_(1) , m_(1), n_(1)],[l_(2), m_(2), n_(2) ],[l_(3),m_(3),n_(3)]]xx [[l_(1),l_(2), 1_(3)],[m_(1) ,m_(2),m_(3) ],[n_(1),n_(2),n_(3)]]` `= [[Sigmal_(1)^(2),Sigmal_(1) l_(2) ,Sigmal_(3)l_(1)],[Sigmal_(1)l_(2),Sigmal_(2)^(2), Sigmal_(2)l_(3) ],[Sigmal_(3)l_(1), Sigmal_(2)l_(3),Sigmal_(3)^(2)]]= [[1,0,0],[0,1,0],[0,0,1]]=I` Hence, matrix A is orthogonal.

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