MATH102 Lecture 1: Linear Systems and Inverses, Matrix Types

Matrix: Additional questions set 1 1. John has inherited $25,000 and put the money in three types of investment a money market account, municipal bonds and a mutual fund. After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutually fund paid 8% annually. His investment in the bonds is s6,000 more than that in the mutual funds. Find the amount John invested in each type of investment. (ay Write down the matrix equation (Ax b)representing the problem. (b) Use GaussJordan method to obtain the inverse of the matrix A in part (a) (c) Use the answer from (b to determine the amount of each type of investment. 15000 25000 ANS 0.06 0.07 0.08 x, 1620 x 8000 2000 L ,J l 6000 0 2 0 and C 2. Let A 0 2 5 a) Find det A and adjoint of A (adj A if (A (BT) -I b) Find B c) Solve A x -2 10 13 -2 33 -10 4 ANS. det A. 20, adj (Al)- 0 10 0 B1- 85 30 0 20 3. For a system of linear equation below where C and D are real constants x, 2x, x 5x, 2x 1 x 2x, 5x2 2x3 x 6 2-3x -6x x, 3x, Cx, 4x 5 Dx a) Write down the matrix equation (Ax b)and the augmented matrix that represents the above system of linear equations b) What are values of C and D that make this system inconsistent? Sasi thon Bland 1703/2016

Write your solution on separate sheets of paper and attach them to this page before handing in. Show your work clearly. Problem: The matrix 1 0 2 1 1 1 2 1 3 3 -10-2 0 1 -1 1 0 1 5 1 9-1-11 2ノ has the reduced row echelon form 1 0 2 0-3 0 0 1 -1 0 2 0 0 0 0 1 -2 0 0 0 0 0 0 1 R- (This is of course easy enough to check, but you are not required to do so.) Use this information to solve the following linear systems without further computations: 2x1+02+33+3x4-10x5-2c6 0 2c1+02+3x3+3c4-10z52 51+2+9x3 4-1152 2T1+2+33+3410 51+2+93- 411

weBWorK : Kim,MAT-24 ×Te Parameterize The 5oluti . D WeBWorK :Lytvak-MAT- L x >c ← C secure https://webworkasu.edu/webwork2/Kim MAT 242 Fall 2017/Chapter 1/7/?key-uENc7HskigosRtSbeyb4WTVF9f9KgRWu&effectiveUser,oremus&user=joremus WeBWork Logged in as joremus Lon Out L MATHEMATICAL ASSOCIATION OF AMERICA webwork / kim_mat 242 fall_2017 chapter 17 MAIN MENU Courses Homework Sets Chapter 1: Problem 7 Chapter 1 Problem 7 User Settings Previous Problem List Next Grades (1 point) Parameterize the solutions to the following linear equation, and write your answer in vector form. Problems 2.33 1.33 Problem 1 Problem 2 Problem 3.. Problem 4. Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14... Problem 15 Problem 16. Solution: Note: You can eam partiaf credit on this problem. Preview My Answers Submit Answers You have attempted this problem 3 times. Your overall recorded score is 0% You have unlimited attempts remaining. Ernail instructor Page generated at oB 29/2017 at 03:39pm MST weBworK⑩ 1996-2016 l theme: meth4 Iww-version: 2.12 I pg-version: 2.121 The weeworK Proiect OType here to search 3:40 PM 8/29/2017