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it\" edition 1.2 #20: Gioose values fork and i: so that the system has (a) no solution, to] a unique solution, and {cl innitely many solutions. Give separate answers for each. 11 312 = 1 23:1 +lu:2 = i: 4" edition 1.2 #22: Mark each of the following statements as true or false. You must provide a reason for your answer. a. The reduced echelon form of a matrix Is unique. it. If every column of an augmented matrix contains a pivot, then the corresponding system is consistent. c The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. d. A general solution of a system is an explicit description of all solutions of the system. e. Whenever a system has free variables, the solution set contains many solutions. 4'\" edition 1.2 #34: [Ml In a wind tunnel experiment. the form on a projectile due to air resistance was measured at differentvelocities: Velocity (100Wsec) o z 4 a a 10 Farceunuib) o 2.9 14.3 39.6 74.3 119 Find an interpolating polynomial of the form p0) = on + a1: + aztz + a3? + aat' + uses for these data and estimate the force on the projectile when the projectile is traveling at 150 ftfsec. What happens if you try to use a polynomial of degree less than 5? 4'\" edition 1.3 #1; Find u + v and u 2v. 1* =61)\" = C?) it\" edition 1.3 #5: Write a system of equations that is equivalent to the given vector equation. \"(Edvziihd 4'\" edition 1.3 #11: Determine if b is a linear combination of o1, rta and a3. \"(sec-scit-:1) 4" edition 1.3 #13: Determine if b is a linear combination of the column vectors ofthe matrix A. 1 Il- 2 3 A=( 3 5).b=(7) 2 8 3 4" edition 1.3 #17: List ve vectors in Spanha, 19;}. For each vector, show the weights on 91 and 172 used to generate the vector. Do not make a sketch. MGM) 2 4'\" edition 1.3 #21: Let u = (fl) and r: = (1 numbers it and it. ). Show that (D is in span{u. v} for all choices of the 4'\" edition 1.3 #27: A mining company has two mines One day's operation at mine #1 produces are that contains 30 metric tons of copper and 6C!) kilograms of silver, while one dafs operation at mine #2 produces are that contains no metric tons of copper and 330 kilograms of silver. Let v: = (63(3)) and v3 = (133(1)). Then v1 and trz represent the output per clay of mine #1 and mine #2, respectively. a. What physical Interpretation can be given to the vector 51);? b. Suppose the company operates mine #1 for x1 days and mine #2 for x; days. Write a vector equation whose solution gives the number of days each mine should operate in order to produce 2&0 tons of copper and 282:! kilograms of silver. Do not solve the vector equation