Ma-1210 Week10 Lab

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Matrix Solutions, Determinants, and Cramer’s Rule Answer the following questions to complete this lab. Show all of your work for each question to get full credit. Matrix Solutions to Linear Systems: 1. Use back-substitution to solve the given matrix. Begin by writing the corresponding linear equations, and then use back-substitution to solve your variables. 10–1301–8001 159–1 = x-13z=15y-8z=9z=-1 = x-13(-1)=15y-8(-1)=9z=-1 = x=2y=1z=-1 x,y,z=(2 , 1 , -1) Determinants and Cramer’s Rule: 2. Find the determinant of the given matrix. 8–2–12 = 8*2 - (-1)(-2) = 16 - 2 = 14 3. Solve the given linear system using Cramer’s rule. 5x –9y= –13–2x+3y=5 Complete the following steps to solve the problem: a. Begin by finding the first determinant D: D= (5*3) - (-2*-9) = 15 - 18 = -3 b. Next, find Dx the determinant in the numerator for x: Dx= (-13*3) - (5*-9) = -39 + 45 = 6 c. Find Dy the determinant in the numerator for y: Dy = (5*5) - (-2*-13) = 25 - 26 = -1 d. Now you can find your answers: X = DxD = 6-3 = -2 Y = DyD = 1-3 = -13 So, x,y=( -2 , -13 ) Short Answer: 4. You have learned how to solve linear systems using the Gaussian elimination method and the Cramer’s rule method. Most people prefer the Cramer’s rule method when solving linear systems in two variables. Write at least three to four sentences why it is easier to use the Gaussian elimination method than Cramer’s rule when solving linear systems in four or more variables. Discuss the pros and cons of the two
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