Solved By Hand

Answer all the question

1. Solve the following systems of linear equations using naive Gaussian elimination method and modified Gaussian elimination method with partial pivoting and compare the component wise error involved in its solutions. a. 0.729x+0.81y+0.9z=0.6867x+y+z=0.83381.331x+1.21y+1.1z=1 b. x12+33=23132+3=1x1+2=3 2. Solve the system, 0.0011+2=1,1+2=2, i) using Gaussian elimination with partial pivoting with infinite precision, ii) using naive Gaussian elimination with 2-digit rounding, and iii) using modified Gaussian elimination method with partial pivoting, using 2digit rounding. 3. Use Gauss-Jordon method to find the inverse of the matrix for the system of linear equations 11/22+1/33=11/211/32+1/43=21/311/42+1/53=3,withfour-digitrounding. 4. Three matrices are defined as [A]=6125184[B]=[40.502][C]=[2321] a. Perform all possible multiplications that can be computed between pairs of these matrices. b. Justify why the remaining pairs cannot be multiplied. 5. Given the system of equations 32+73=41+223=05122=3 a. Compute the determinant. b. Use Cramer's rule to solve for the xs. c. Use Gauss elimination with partial pivoting to solve for the xs. As part of the computation, calculate the determinant in order to verify the value computed in (a). d. Substitute your results back into the original equations to check your solution. 6. Apply gauss Jordan method to solve the system of equations: x+y+2z=43x+y3z=42x3y5z=5 7. Consider the system of equation of the form AX=B, where A=421132212 X=xyz and B=737. Find by using Gauss-jordan method. a. A1 b. The numerical solution of the given system