5. Consider the linear system 240 319.5 $1 _ 3 179.5 240 $2 _ 4 ' The exact solution, as you can verify easily, is x = [8,6]. (a) (10 pts.) Apply naive Gaussian elimination to solve the system but using 4-decimal digit with rounding to nearest. Remember, you must round to 4 digits after each arithmetic operation. (b) (5 pts.) Calculate the relative error lh'si'l'llg in the computed solution. 00 (c) (10 pts.) For the airthmetic used above t = 4 hence the machine roundo' unit is u = % x 10'3 obtained from the general formula u = t'l. Compare the error in (b) to u. How do you explain the fact that the error is much larger than u? Hint: Compute the condition number moo (A) of A