In Problems 17–20 the given
18.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 3. Let a ER and let: 1 -2 2 4- ( -² ) A = 1+ a 4+ a -2. a " a a 2 - a You may assume without calculation that ch₁(x) = (x − 2)²(x − 3). For which values of a, is A diagonalisable?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_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_forward
- 2a. 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_forwardA Moving to another question will save this response. Question 2 Statement 1: x+y z (x+y) (x+z) Statement 2: x Oy= (x +y) (x y) Statement 1 : True Statement 2 : False Statement 1 : False Statement 2: True Statement 1: False Statement 2 : False Statement 1: True Statement 2: True A Moving to another question will save this response.arrow_forwardCompute u + v, 2u – v, 3u – 2v, and 0 – 3v if (a) u =| 2 3 2 (b) u= = -3 (c) u = 1 4arrow_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 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_forward14. Assume x E R. Give the matrix associated with the quadratic form 10(x,) - 5x,x2 + 6(x,).arrow_forward
- 7. Problem 8.3.14: Determine whether the given set of vectors is linearly dependent or linearly independent. U1 = (2,1,1,5), ūz = (2,2,1,1), ūz = (3,–1,6,1), ū4 = (1,1,1,–1)arrow_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_forward4. Find the standard matrix for T where T(a) (2x,+x 1-2x2).arrow_forward
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