The linear system xi + 2X2 - 2X3 = 7, X] + X2+ X3 = 2, 2xi + 2x2 + X3 = 5 has the solution (1, 2, 1)'. a. Show that p(Tj) 0. Use the Jacobi method with x <0) = 0 to approximate the solution to the linear system to within ID-5 in the 1^ norm. Show that p(Tg) = 2. Show thatthe Gauss-Seidel method applied as in part (b) fails to give a good approximation in b. c. d. 11. 25 iterations.
Lecture 4: Inverse Functions (Section 1.5) Read pp. 33−37 of the textbook and then ﬁll out the ﬁrst and half pages (before the ﬁrst example) below before class. 1. One-to-one functions Def. Au fn f is called a one-to-one function if for any x1and x i2 the domain: if 1 ▯= x2then • Horizontal Line Test 2. Inverse functions Def. Let f be a one-to-one function with domain A and range B.T nisaqirnt f−1 : B → A which assigns to each y in B the unique x value inA given by f−1(y)= x if and only if • If (x,y)iapitntegphof f(x), then Therefore, the graph of f−1 is the graph of f reﬂected through the line