In Problems 21–24 verify that the
22.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 9. 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_forwardSuppose a, = (1 -1 1 1) 5. az = (1 0 1 0) %3D %3D az = (1 1 1 1)''a¸ = (3 2 3 0)" - Please find out whether a1,a2,a3,&4 are linear independent or not?arrow_forward4. Find the standard matrix for T where T(a) (2x,+x 1-2x2).arrow_forward
- 1. Find the linearization of x3 − x at a = 2.arrow_forward1. 2. 3. Write v as a linear combination of u and w, if possible, where u = (2, 3) and w = (1, -1). (Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE.) v = (-2, -3) V = Solve for w where u = (1, 0, -1, 1) and v = (2, 0, 3, -1). w + 2v = -4u W = Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, -1, 3), (5, 0, 4)) (a) z = (7, -6, 14). Z= (b) v = V = (c) w = (3,-9, 15) W = (d) v = (18, - 1, 59) )$₁ U= $₁ + u = (2, 1, -1) )$₁arrow_forward3.16. Let P-1 and 2-11] = Q = Find a 2 x 2 matrix X such that PXQ: = -4 1] [2]arrow_forward
- 7. Find two linearly independent solutions of y" + 3ay = 0 of the form y₁=1+ a32³ +as+... 32=2+b₁¹+b727 +.... Enter the first few coefficients: as 11 ag= b₁ == 41 (numbers) (numbers) (numbers) ›(numbers)arrow_forwardProblem 16 (#2.3.34).Let f(x) = ax +b, and g(x) = cx +d. Find a condition on the constants a, b, c, d such that f◦g=g◦f. Proof. By definition, f◦g(x) = a(cx +d) + b=acx +ad +b, and g◦f(x) = c(ax +b) + d=acx +bc +d. Setting the two equal, we see acx +ad +b=acx +bc +d ad +b=bc +d (a−1)d=(c−1)b That last step was merely added for aesthetic reasons.arrow_forward11.3 11.4: Problem 7 Find the linearization L(x, y, z) of the f(x, y, z) = 2/ x³ + y³ + z³ at the point (1, 2, 3). Answer: L(x, Y, z) =||arrow_forward
- 4. (S.10). Use Gaussian elimination with backward substitution to solve the following linear system: 2.r1 + 12 – 13 = 5, 1 + 12 – 3r3 = -9, -I1 + 12 +2r3 = 9;arrow_forwardThe matrix that projects onto the line y = -x is X 0.6 0.8 0.8 -0.6arrow_forward9. discuss the behavior of the dynamical system Xk+1= Axk where -0.31 (@) A = [ (b) A = ["0.3 11 1.5 0.3 (b) A = 0.3 1 3Darrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage