1. Ends of a wire grid are kept at a constant temperature, as shown. The temperature of each interior point is the average of the temperature of its neighbors. For example, T1=410+T2+T6+10 The corresponding system of linear equation we would solve to find the temperatures of the interior has augmented matrix (for variables T1,T2,T3,T4,T5,T6 ) equal to: 410001141010014100001410010141100014201060803040 (a) Write down the commands you would enter in SAGE to find the RREF. (b) Enter those commands and Evaluate SAGE. The answer will have rather annoyingly large fractions so replace the command A.rref () with the extended command Arref(). n(). Now Evaluate SAGE again and write down the answer, which is a decimal approximation of the RREF. Round to the nearest one decimal place. (c) What is the corresponding (approximate) solution to the system? Don't forget the variables are T1,T2,T3,T4,T5,T6 (d) We said earlier that T1 should be the lowest temperature and T4 should be the highest temperature. Did it turn out that way? (Hint: it should!)