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Unformatted text preview: S : R n → R n such that S ( T ( x )) = x and T ( S ( y )) = y for all x and y in R n . S is called the (function) inverse of T . Suppose the linear transformation T is given by T ( x ) = A x for some matrix A . Then T is invertible exactly when A is invertible, and in this case the function inverse of T is given by S ( y ) = A-1 y . EXAMPLES. Is 2 6 4 0 7 8-6 5 invertible? Do as little work as possible! A matrix is lower triangular if the entries above the main diagonal are all 0’s. When is a square lower triangular matrix invertible? Why? Show that if A and B are square and AB is invertible, then so is B . HOMEWORK: SECTION 2.3...
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