Problem 2 (a). Let the function F:RnRm be given by F(x)=Ax+d, where A is an mn matrix and d is a vector in Rm. Show that F is continuous on Rn. (Hint: The proof here, using , is very similar to the proof that a linear transformation is continuous on Rn, as done in the lecture on Wednesday 16 November and in the text in Theorem 3.13 on page 85 . Your argument should also contain two cases, the case where A is the zero matrix and the case where A=Omn, and you may freely use the fact that constant functions are continuous on all of Rn.) [10 marks] Problem 2 (b). Consider the function F([x1x2])=103214[x1x2]+101. Let the limit of F as x[22] be called L. What is L ? (Hint: F is defined at b=[22], and so F can be evaluated directly at this input vector.) How close should x be to [22] in order to ensure that the output of F is within 0.1 of L ? (Hint: Here, =0.1. What is the corresponding ? The relationship between and should be given to you by your work in part (a) of this problem.) [2 marks]