Let us imagine that we are studying a physical system that gets hotter over time. Let us also suppose that we expect a linear relationship between time and temperature. That is, we expect time and temperature to be related by a formula of the form T= at + b| where T is temperature (in degrees Celsius), t is time (in seconds), and a and b are unknown physical constants. We wish to do an experiment to determine the (approximate) values for the constants a and b. We allow our system to get hot and measure the temperature at various times t. The following table summarizes our findings t (sec) 0.5 T (C) 32.0 Find the least squares solution to the linear system that arises from this experiment. 1.1 33.0 1.5 34.2 2.1 35.1 2.3 35.7