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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 11. 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_forwardProblem 25. Suppose yı (x), y2(x), and y3(x) are three different functions of x. The vector space they span could have dimension 1, 2, or 3. Give an example of y1, y2, y3 for each case.arrow_forwardProblem 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_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_forwardPart 3&4 needed to be solved correctlyarrow_forwardPlease all solve the issuearrow_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_forward3. Suppose A = 3 1 1 -2 (a) Find a vector X E R² such that AX = (b) Find a vector X € R² such that AX = B 9arrow_forwardThe matrix that projects onto the line y = -x is X 0.6 0.8 0.8 -0.6arrow_forward
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