14111cn2.14-15

# 14111cn2.14-15 - 32 56 3 a ²-4 ± 4 / 11 1 / 11-3 / 11 2 /...

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c ± Kendra Kilmer August 18, 2011 Section 2.6 - The Inverse of a Square Matrix Deﬁnition: Let A be a square matrix of size n . A square matrix A - 1 of size n such that is called the inverse of A . Example 1: Show that the matrix A = ± 1 2 3 4 ² has as its inverse A - 1 = ± - 2 1 3 / 2 - 1 / 2 ² Deﬁnition: Every square matrix does not have an inverse. We say that a matrix is singular if it does not have an inverse. If it does have an inverse, we say that it is nonsingular . You are not responsible for calculating inverses by hand. In the next example, I will show you how to ﬁnd the inverse of a matrix on the calculator along with matrix multiplication. Example 2: Given A = 1 2 5 - 2 4 1 1 3 2 B = 1 - 3 0 5 0 1 - 2 8 3 Compute: a) AB b) A - 1 Example 3: Find a , b , and c in the following matrix equation. ± -

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Unformatted text preview: 32 56 3 a ²-4 ± 4 / 11 1 / 11-3 / 11 2 / 11 ²-1 = ± 3-7 2 b + 7-2 3 1 ² 4 c-1 3 5 2-4 14 c ± Kendra Kilmer August 18, 2011 Using Inverses to Solve Systems of Equations If AX = B is a linear system of n equations with n unknowns where A is the coefﬁcient matrix, X is the matrix of unknowns, and B is the constant matrix and if A-1 exists, then is the unique solution of the system. Example 4: Solve the following system: z = 4 x-y 3 x = 12-4 z y + 3 z = 6 Example 5: Solve the following system: x 1 + x 2 + x 3 = 5 x 1-x 2 + x 3 =-3 x 1-2 x 2-x 3 =-1 Section 2.6 Highly Suggested Homework Problems: 3, 9, 11, 19, 41, 43, 51 15...
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## This note was uploaded on 03/27/2012 for the course MATH 141 taught by Professor Jillzarestky during the Fall '08 term at Texas A&M.

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14111cn2.14-15 - 32 56 3 a ²-4 ± 4 / 11 1 / 11-3 / 11 2 /...

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