Stitz-Zeager_College_Algebra_e-book

# We when x one solution is 2 5 5 4 5 5 similarly we

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Unformatted text preview: t= The region where 3.5s + 1.5t − 4 > 0 8 3 The region for our parameters s and t. 16 7 t 8.4 Systems of Linear Equations: Matrix Inverses 8.4.1 505 Exercises 1. Find the inverse of the matrix or state that the matrix is not invertible. (a) A = (b) B = 12 −7 −5 3 (c) C = 6 15 14 35 (d) D = 12 34 2 −1 16 −9 4 3 (f) F = 1 1 (g) G = 2 3 6 −3 4 −3 2 6 23 3 11 4 19 1 0 −3 2 −2 8 (h) H = −5 0 16 1 0 4 3 0 4 3 (e) E = 2 −1 −3 2 −5 0 7 0 1 2. Use a matrix inverse to solve the following systems of linear equations. 3x + 7y = 26 5x + 12y = 39 (a) 3x + 7y = 0 5x + 12y = −1 (b) 3x + 7y = −7 5x + 12y = 5 (c) 3. Use the inverse of E from Exercise 1 above to solve the following systems of linear equations. 3x + 4z = 1 2x − y + 3z = 0 (a) −3x + 2y − 5z = 0 3x + 4z = 0 2x − y + 3z = 1 (b) −3x + 2y − 5z = 0 (c) 3x + 4z = 0 2x − y + 3z = 0 −3x + 2y − 5z = 1 4. This exercise is a continuation of Example 8.3.3 in Section 8.3 and gives another application of matrix inverses. Recall that given the position matrix P for a point in the plane, the matrix RP correspond...
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