In Problems 21–24 verify that the
22.
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First Course in Differential Equations (Instructor's)
- What can you conclude about the values of the quadratic form Q(x)?arrow_forward5. 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_forward3. In M3x2(F), prove that the set { ( ) ( ) ( ) ( ) ( ) } " 0 0 1 is linearly dependent.arrow_forward
- 8. 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_forward1. 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_forward2. Find the equation f(x) = ax+b of the least square line for the points (1,0), (−1, 2), (2, 1).arrow_forward
- In Problem. -24, the given vector functions are solutions to a system x' (t) = Ax(t). Determine whether they form a fundamental solution set. If they do, find a fundamental matrix for the system and give a general solution. -E]. et 24. x₁ = X2 sint COS [ -sint_ X cost sin/ COSTarrow_forward( x1=0 , x2=2 ) Solve by using MATLABarrow_forward5. Find two linearly independent polynomials orthogonal to p(x) = 1 + x² using the inner product from problem 2.arrow_forward
- 10. Find the general solution of the system of differential equations 3 -2 -2 d. X = -3 -2 -6 X dt 3 10 1 + 2tet + 3t?et + 4t°et 3 1 -3 Hint: The characteristic polymomial of the coefficient matrix is -(A- 4)²(A- 3). Moreover (:) 2 1 Xp(t) = t²et +t³et +t'e3t -1 -1 -3 is a particular solution of the system.arrow_forward7. Consider the invertible matrix It is given that A-1 = b11 b21 b12 b22 2 -- (EE) b31 b32 1 2 -1 -- (7) = 2 -2 A 0 1 1 (a) Find the entry b21 of A-¹ using the adjoint formula. X (b) Solve the linear system AX + 2B = 0, where X = y B = " and 0 is the zero Z matrix of the appropriate size.arrow_forward1.4 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_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage