In Problems 17–20 the given
17.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 1. 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_forward11. If a and B are the roots of the quadratic 3.x2 – 4x + 6 = 0, find the value of (+) 2 :G7) -24° will be 12. For matrix A =arrow_forwardQ.2 The given vectors are solutions of a system X'= AX . Determine whether the vectors form a fundamental set on the interval (-∞,0). 1 1 2 - 2 le4 31 ,X3 = - 2 X, = 6. X, = 3 -3arrow_forward
- Question 9 Find all the roots of z3 – 3(5 +j) = 0 and give the answers in rectangular form. Question 10 Use Crammer's rule to solve the following linear system for y only. 2x – 3y = 3 – z 4x +y = -4 = 3y + z-2 İLIFE Digitalarrow_forward2. Which of the following is a general solution to the following: x²y" + xy' + (36x² - 1) y (Hint: As discussed in the lecture, use Y, only when J, and J-, are linearly dependent). A. y = c₁J₁(2x) + C₂J_1(2x) 6 B. y = C₁J₁(x) + C₂Y₁(x) 3 3 C. y = c₁₂/₁(6x) + C₂Y₁(6x) 0 D. y = c₁J₁(6x) + c₂] _1(6x) 2arrow_forward4. Find the standard matrix for T where T(a) (2x,+x 1-2x2).arrow_forward
- 14. Assume x E R. Give the matrix associated with the quadratic form 10(x,) - 5x,x2 + 6(x,).arrow_forward1. Show that the functions e*, e2*, e3* are linearly independent. Show Complete Solution Answer: W = 2e6x + 0arrow_forward2 5 3 1 For the linear system AX=B, if A-1=1 0 1 and B=0 012 then the unknowns vector X=arrow_forward
- 4. Verify that the given vectors of this system of ODEs are solutions, and use the Wronskian to verify that they are linearly independent. Write the general solution. e2t - (³ 5 x' = 3 -1 -3 X, X1 = 9 x2 = ( e-2t 4) 5e-2tarrow_forwardIn Exercises 11–14, find parametric equations for all least squares solutions of Ax = b, and confirm that all of the solutions have the same error vector. 1 3 1 12. A = -2 -6 |; b = ! 0 3 9. 1arrow_forward2a. Write a MATLAB command that creates a row vector u that has the elements: cos( 3e y 19π 4 TT -2e, log10 (210), -60, 4|sin (-5)| Where | sin(x) is the absolute value of the sin(x). Then write the command to find the maximum value of v. 2b. Write MATLAB commands that assign 7 to variable x and 11 to variable y, create a column vector w that has the following elements, and then compute the average value of the elements: x! In(2y + x), √√x² + y², √(x + y)²-(y - x)² Where x! is factorial of x, for which you can use MATLAB built-in function, and ln(x) is the natural logarithm of x.arrow_forward
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