\fIn a grid of wires, the temperature at exterior mesh poins is maintained at constant values as shown in the figure. When the grid -178 is in thermal equilibrium, the temperature at each interior mesh point is the average of the temperatures at the four adjacent -176 points. For instance, TI = T2 + T3 + 20- 170 4 Find the temperatures Ti, T2, T3, T4, when the grid is in thermal equilibrium. T1 = To = T3 = TA =Let v1, v2, '03 be the vectors in R3 defined by 18 *2 716 '01 5 '02 12 113 17 728 14 14 (a) Is {111, oz, 123} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a nontrivial (not all zero coefficients) linear combination of U1, U2, and v3 0: 191+ EEE 112+ '03 (b) Is {111, 112} linearly independent? Write all zeros if it is or if it is linearly dependent write zero as a non-trivial (not all zero coefficients) linear combination of 111 and '02. o l | G H + e N (c) Type the dimension of span{v1, 112,113}