Let A be an n n matrix and b be in Rn. If Ax = b has aunique solution, show that A must be invertible.

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