In Problems 21–24 verify that the
22.
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
- Problem 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_forwardThe matrix that projects onto the line y = -x is X 0.6 0.8 0.8 -0.6arrow_forward
- 5. Given the system X" - ()* 10 2 (a) Find the general solution. (b) Find the solution that satisfies the initial condition (x(0), y(0)) = (0, –7). Report your solution as one vector.arrow_forward8. Find all values of h, if any exist, such that b a linear combination of v1 and v2? 1 h (a) vị = V2 = b 8 1 (b) vị = b = h V2 =arrow_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
- 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_forward1. Solve for x and y in xy + 8 + j(x²y + y) = 4x + 4 + j(xy² + x) A. 2, 2, B. 2,3 C. 3, 2 2. Determine the principal value of (3 + j4)¹ +² +j2 A. 0.42+j0.56 C. -0.42-j0.66, B. 0.42+j0.66 D. 0.42-j0.66 3. Using the properties of complex numbers. determine the two square roots of 3-j2 A. +1.82+j0.55, C. 1.82 + j0.55 B. +1.82±j0.55 D. +1.82 + j0.55 4. Evaluate: BE CALC 3-14 3+14 + 3+j4 3-j4 A. 2.44 +j4/ B. 2.44-j4 C. -2.44 + j4 D. 2.44 +j5 Evaluate log; (3 + j4). A. 0.6+j1.02 C. -0.6-j1.02 B. -0.6+j1.02 D. 0.6-j1.02, 6. The following three vectors are given; A = 20 +j20, B = 30/120° and C= 10+ j0, find AB/C C. 95/-50° B. 85-75% A. 70/45° D. 75/70" 7. If 100+5x/45° = 200/-e. Find x and 8. A. 24. 23.28 B. 23.28. 32.3° C. 23.28. 24.3% D. 23, 42.8° 8. Determine the principal value of cosh' (j0.5). A. In (1+j5) C. In j5 B. In (1± √5), D. In j(1 + √5) 2 5 1 = 9. In A-2B-C=0. if A= 2B-C-0. if A- and B-₁ find C |² -1 3 2 3 8 -3 8 3 91 C. A. 3 0 0 -3 -8 -8 -3 3 D. B. | 3 0 -3 10. Solve for a and b…arrow_forward3,2 3.2 X(x²-1)-y=xy ;y(2)=-arrow_forward
- 1.4 Which of the following equations are linear? (iii) x = -7y + 3z (i) x + 5xy – 2z = 1 1 (v) VTx + v2y + (ii) x + 3y + z = 2 (iv) e" – z = 4 z = 71/3 (a) (i), (iii) and (v) (b) (iii) and (iv) (c) (ii), (iii) and (v) (d) (ii) and (iii) (e) None of the above.arrow_forward1. 2. Find a 2x2 matrix A such that A² = 1 4 -1 Find A when (34)¯¹ : 23arrow_forward18.- Define the symmetric matrix corresponding to the following quadratic form: F(x, y, z)= x² + z²-2xy+xz - 2yzarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage