Consider the square plate shown in the figure, with the temperatures as indicated on each side. Under some circumstances it can be shown that the approximate temperatures u1, u2, Uz

Extracted text: Consider the square plate shown in the figure, with the temperatures as indicated on each side. Under some circumstances it can be shown that the approximate temperatures u1, u2, Uz < and="" ug="" at="" the="" points="" p,="" p2,="" p3,="" and="" p4,="" respectively,="" are="" given="" by="" uz="" +="" u4="" +="" 100="" +="" 100="In" 200="" +="" uz="" +="" u1="" +="" 100="" 4="" u2="4" 200="" +="" 100="" +="" u4="" +="" uz="" ug="4" uz="" +="" 100="" +="" 100="" +="" u1="" u4="4" (a)="" show="" that="" this="" system="" of="" equations="" can="" be="" written="" as="" the="" matrix="" equation="" -4="" 1="" 1="" -200="" -300="" 1="" -4="" 1="" 1="" -4="" 1="" u3="" -300="" 1="" 0="" 1="" –200/="" (b)="" solve="" the="" system="" in="" (a)="" by="" finding="" the="" inverse="" of="" the="" coefficient="" matrix.="200" m="" 100="" u="100" p.="" 4="">