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Writing a Linear Combination In Exercises
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Elementary Linear Algebra (MindTap Course List)
- Review Exercises Writing a Linear Combination In Exercises 9-12, write v as a linear combination of u1,u2 and u3, if possible. v=(3,0,6),u1=(1,1,2),u2=(2,4,2) and u3=(1,2,4)arrow_forward20+ 80 X1 A C X3 x2 B X4 -. a. Find the general traffic pattern in the freeway network shown in the figure. (Flow rates are in cars/minute.) b. Describe the general traffic pattern when the road whose flow is x4 is closed.arrow_forwardUsing mapping notation, determine the linear function machine that generates the point (– 2,9).arrow_forward
- The table shows the numbers of visitors y (in thousands) to one country from another country from 2012 through 2014. Visitors, y (in thousands) Year 2012 1476 2013 2014 1805 2186 (a) The data can be modeled by the quadratic function y = at? + bt + c. Write a system of linear equations for the data. Let t represent the year, with t= 12 corresponding to 2012. = 1476 = 1805 = 2186 (b) Use the matrix capabilities of a graphing utility to find the inverse of the coefficient matrix of the system from part (a). (c) Use the result of part (b) to solve the system and write the model y = at2 + bt = c. (d) Use the graphing utility to graph the model with the data.arrow_forwardFindu + v, 2v,u-v, and 3u - 2v. u = (2, −4, 5, 2), (b) 1+v= (d) 2V = (c) u-v= Bu-2v - v = (0, 2, 2, 3)arrow_forwardThe statement is either true in all cases or false. If false, construct a specific example to show that the statement is not always true. If V₁, ..., V4 are in R4 and V3 = 2v₁ + V₂, then {V₁, › V2, V3, V4} is linearly dependent. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. True. Because V3 = 2V₁ + V₂, V4 must be the zero vector. Thus, the set of vectors is linearly dependent. 1 B. True. If c₁=2, C₂ = 1, c3 = 1, and c4 = 0, then c₁ V₁ + ··· + C4V₁ = 0. The set of vectors is linearly dependent. .. C. True. The vector v3 is a linear combination of v₁ and v₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent. O D. False. If v₁ = , V₂ =₁ V3 = " and V4 = 1 2 1 2 IN then V3 = 2v₁ + V₂ and {V₁, V₂, V3, V4} is linearly independent.arrow_forward
- can you answer?arrow_forwardchoice section 37. What is the equation of the line that passes through the coordinates (-1, -2) and (3, 10)? A. no solution B. infinite solutions C. (-1, 6) Powered by Linkit!arrow_forwardDegrees Earned The number of postsecondarydegrees earned, in thousands (including associate’s,bachelor’s, master’s, first professional, and doctoral degrees), can be modeled by y = 3.980x2 -17.597x + 2180.899, where x is the number of yearsafter 1990. If this model is accurate, during what yearsfrom 1990 on would the number of postsecondarydegrees earned be less than 3500 thousand?arrow_forward
- Explain the determine yellowarrow_forward2) A regression in statistics is statistical analysis that assess the relationship between two variables. The calculation is used to determine the relationship between two variables. You are given the task to determine the relationship between student's study hour and their grades achieved. You must answer these questions: I. Sketch a scatter plot for a data. II. Find the equation of the least squares line that will enable us to predict a student's grade based on his or her study hour. Interpret the result. III. Calculate the coefficient of determination and coefficient of correlation.arrow_forwardmarket study determined that for each unit a good is sold Hi-Fi electronics the unit price of it falls by $ 380 [MU]. Yes when not units of this good are sold, the unit price is $ 8,360 [MU]., determine: a) The model or function that relates the unit price X of the good in relation to the quantity sold and, knowing that it is linear. b) How many units of the good must be sold, so that the unit price is $ 2660 [UM]. c) How many units must be sold so that each one is exactly free? one of them? d) Using a graph, determine the domain and economic path of the function of unit pricearrow_forward
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