Problem: Use the Bisection Method to find the two real numbers x, within six cor

Question

Problem: Use the Bisection Method to find the two real numbers x, within six correct decimal places, that make the determinant of the matrix A = 0 1 2 x 3 4 x 5 6 x 7 8 x 9 10 11 equal to 19. For each solution that you find, test it by computing the corresponding determinant and reporting how many correct decimal places (after the decimal point) the determinant has when your solution x is used. Not that when you use your solutions to calculate the determinant, you will not necessarily have six correct decimal places!

Explanation / Answer

Solution: First, use Maple: with(linalg): A:=matrix(4,4,[1,2,3,x,4,5,x,6,7,x,8,9,x,10,11,12]); f:=det(A); 2 4 -2475 - 202 x + 1404 x + x plot(f-1000,x=-20..15); We’ll be using -3475 for our constant, since we’re trying to find where the determinant is 1000. We see that the zeros are between -20,-15 and 5, 15. Therefore, I’ll use Matlab with intervals [2, 4] and [4, 6] (many choices possible): format long f=inline(’x.^4-202*x.^2+1404*x-3475’); y=bisect(f,5,15,0.5e-6); Finished after 24 iterates y = 9.70829933881760 y=bisect(f,-20,-15,0.5e-6); Finished after 23 iterates y = -17.18849807977676

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