Homework

1. A system of linear equations with more equations than unknowns is sometimes called overde- termined. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns. 2. Suppose a 3 x 5 coefficient matrix for a system of equations has 4 pivots. Is the system consistent? If the system is consistent, how many solutions are there? 3. Write down all the possible reduced row echelon forms for a 3 x 3 matrix. 4. Given the system of equations below: 2 1 + 7202 + 3203 + 204 + 725 + 206 = 7 3x1 + 4x2 - 723 - 424 + 525 +14x6 = 11 -4x1+ 2 + 823 + 624 + 925 + 526 = 40 5x1 + 32 + 923 + 24 + 825 + 7206 =-320 9x1 - 2x2 + 323 + 424 - 325 + 96= 0 3x1 - 22+ 223 + 24-25+ 326=50 Answer the following questions: (a) Use technology to solve the system of equations. Options include Excel (free with a SJCC student account), or other math software (do not pay for the math software!). Your answer must be accurate to four decimals. (b) Explain what technology you used, and what was good and bad about it