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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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