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Consider the following vectors. -=[B]. = 2 V = 2 W = 3 []. i. There is a unique solution. ii. There is more

  

Consider the following vectors. -=[B]. = 2 V = 2 W = 3 []. i. There is a unique solution. ii. There is more than one solution. iii. There is no solution. z = [] (a) Write the vector equation you would need to solve to determine if Z is in the span{, V, w}. (b) Write the system of equations that has the same solution as the vector equation you wrote in part 2a. (c) Which of the following describes the solutions to your equations from 2a and 2b? Explain your choice. Give an example of one or more solutions if possible. Otherwise, make it clear why this is not possible. 3. Construct a set of vectors in R that satisfy the following requirements. If no such set exists, explain why. Use vectors whose components are given numbers. (a) The set contains one vector that spans R. (b) The set contains two vectors that span R. (c) The set contains three vectors that do not span R. (d) The span of the set contains one vector in R. 4. How many vectors must be in the following sets? Explain. (a) The set is linearly independent and spans R. (b) The set is linearly independent and does not span R. (c) The set is linearly dependent and spans R. 5. Consider A (a) For what value(s) of k is we span{u, v}? (This notation means that w is a vector in the span of and v) Explain how you know. (b) For what value(s) of k is the set {., V, w} linearly dependent? Explain how you know 1 = 2 -4 V=-8 12

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