(a) Given an arbitrary set of numbers M Icirc plusmn Icirc sup2 Icirc plusmn 0, , 3 Icirc sup2 0, , 3 and two arbitrary sets of vector components A Icirc frac14 , Icirc frac14 0, , 3 and B Icirc frac12 , Icirc frac12 0, , 3 , show that the two expressions And Are not equivalent (b) Show that A Icirc plusmn B Icirc sup2 Icirc middot Icirc plusmn Icirc sup2 A0B0 A1B1 A2B2 A3B3 MaBA B

Question: (a) Given an arbitrary set of numbers {MÎ±Î² ; Î± = 0, . . . , 3; Î² = 0, . . . , 3}

(a) Given an arbitrary set of numbers {MÎ±Î² ; Î± = 0, . . . , 3; Î² = 0, . . . , 3} and two arbitrary sets of vector components {AÎ¼,Î¼ = 0, . . . , 3} and {BÎ½ , Î½ = 0, . . . , 3}, show that the two expressions

And

Are not equivalent.
(b) Show that
AÎ±BÎ²Î·Î±Î² = ˆ’A0B0 + A1B1 + A2B2 + A3B3.

MaBA B

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