In Problems 17–20 the given
19.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- Q.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_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_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_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_forward5. Find the cofactors and the adjoint matrix of A where (1 1 -1 b) A =| 2 3 (7 0 -1 a) A = - 2 0 - 2 4 -3 5 4 5 6 2arrow_forward
- 14. Assume x E R. Give the matrix associated with the quadratic form 10(x,) - 5x,x2 + 6(x,).arrow_forward7. 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_forwardQuestion 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_forward
- 1.5.17 Suppose the solution set of a certain system of linear equations can be described as x, = 5+. 4x3, X2 = - 6 – 7x3, with x3 free. Use vectors to describe this set as a line in R°. %D Geometrically, the solution set is a line through || parallel toarrow_forward1. (5pts) Solve the following system T1 + 2x2 – 13 + 3x4 4 2.x1 + 4x2 – 2x3 + 7x4 10 -x1 + 2x2 + x3 – 4r4 -6 Write the solution set in parametric vector form. ||||arrow_forwardThe matrix that projects onto the line y = -x is X 0.6 0.8 0.8 -0.6arrow_forward
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