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.
15.
Want to see the full answer?
Check out a sample textbook solutionChapter 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
- 2. Find the solution set to the following system of linear equations using Gauss-Jordan elimination. (2.x1 + 7x2 – 12.x3 = -9 x1 + 2x2 – 3.x3 = 0 3x1 + 5x2 – 7x3 = 3 - Determine the rank of the coefficient matrix and the augmented matrix.arrow_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_forwardIn Problems 26–28, find the value of each determinant. |2 1 28. 5 0 2 6 1 4 0 -3 3 4 26. 1 27. -1 2 6 3 4 1 3arrow_forward
- 3. Illustrate the Gersgorin theorem by the matrix 1 2 | 1+ 2i A = -1 1 -2 – 2i - -Narrow_forwardForm a coefficient matrix for the following linear system of equations: √x + 16 y = = 11 U x + 2y = -1. [26 11] 1 -1 [161] [11] Hi 0 [1¹9]arrow_forward1. 2. Find a 2x2 matrix A such that A² = 1 4 -1 Find A when (34)¯¹ : 23arrow_forward
- 9. (a) Evaluate the matrix product Ax, where A = 1. and x = 3 Hence show that the system of linear equations 7x + 5y = 3 x + 3y = 2 can be written as Ax b where b = %3D (b) The system of equations 2r + 3y – 2z = 6 x– y + 2z = 3 4x + 2y + 5z = 1 can be expressed in the form Ax = b. Write down the matrices A, x and b.arrow_forward3. If A= 3 4, B= FA-1-30-1.00 -5 and D=10 L5 6 [a b₁ E1- Le , find a matrix C= c d such that 3A + B - 2C= D.arrow_forward46. (a) Show that the jth column of the matrix product AB is equal to the matrix product Ab;, where b; is the jth column of B. It follows that the product AB can be written in terms of columns as AB =[Ab₁ Ab₂ Ab,].arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning