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In problem 15–18 use the method of Example 2 to compute eAt for the coefficient matrix. Use (1) to find the general solution of the given system.
17.
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Chapter 8 Solutions
Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
- 1.3.5 Write f= x + 10x,x2 + x as a difference of squares, and f= xí+ 10x1x2 + 30x as a sum of squares. What symmetric matrices correspond to these quadratic forms by f = x' Ax?arrow_forwardIn Problems 7–14, find the value of each determinant.arrow_forward5. Given the matrix A=[²1] (a) Find the value of x that makes A singular. (b) Find the value of x that makes A-1 = A (i.e, that makes the matrix equal to its own inverse).arrow_forward
- 2.2. Consider the following matrix Y and matrix Z. Each column represents a particular meat industry. industry for beef, pork and chicken: [0.2 0.3 0.21 Y= 0.4 0.1 0.3 [0.3 0.5 0.2] [150] Z= 200 [210] For industries for beef, pork and chicken determine the total demand given by matrix Y and matrix Zarrow_forward3. Q1: Given A = -1 4 3 3. find the matrix X if 2xT-AB = -2 B = 1 -3arrow_forward9. P = 15 -4 -7 2e31 – 8e- -4e31 + 2e- ž(1) = | 3e3t – 20e- -6e31 + 5et Show that x1 (t) is a solution to the system x = Px by evaluating derivatives and the matrix product -4 ž(1) = | 15 -7 Enter your answers in terms of the variable t. Show that x2(t) is a solution to the system x' = Px by evaluating derivatives and the matrix product 9. 3(1) = | 15 -4 X2(t) -7 Enter your answers in terms of the variable t.arrow_forward
- 1. 2. 3. For which values of a and b is the following system of equations inconsistent. x+2y3z = 4 3x = y + 5z = 2 4x + y + az = b (a) a= 2 and b = 6; (d) a = 1 and b = 3; (d) A = Find the standard matrix for the operator on R² which contracts with factor 1/4, then reflects about the line y = x. 0 (a) A = 1/4 0 (₁/11) ( 0 1/4 1/4 ¹/4) 0 (b) a = 2 and b = 6; (e) None of these. (c) a 2 and b = 6; 0 1/4 - (¹/4) 0 (e) None of these (b) A = (e) None of these (c) A = The linear operator T : R³ → R³ is defined by T(x₁, x2, X3) = (W₁, W2, W3), where w₁ = 2x₁ + 4x2 + x3; W₂ = 9x2+2x3; W3 = 2x1 8x2 - 2x3. Which of the following is correct. (a) T is not one to one. (b) T is one to one but the standard matrix for T-¹ does not exist. (c) T is one to one and its standard matrix for T-¹ is (d) T is one to one and its standard matrix for T-¹ is HOLI 0 1 (88) 0 3 0 1 3 3 WIN - WIN 3 0 1 3 1 -4 3 -3 2 -3 1623arrow_forward7. Let A be a matrix with a row consisting of all zeroes. If B is a matrix such that AB is defined, which of the following is always true? 8. Given the matrix B = 1 1 11 Which of the following (233) (a) 3 2 3 332 matrices solves X in the matrix equation X+13= 2(X - B)? (211) (d) 1 2 1 112 (322) (b) 2 3 2 2 2 3 (122) (c) 2 1 2 2 2 1arrow_forward2. (a) Find the condition number of the coefficient matrix in the system X1 (1461) (²2) = (2²6) X2 as a function of d > 0. (b) Find the error magnification factor for the approximate root xa = (-1,3+6).arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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