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For Problems 9-14, determine whether the given set
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- For each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two. (a) (-2,0,3) ,(1,3,0),(2,4,-1) (b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1) (c) (3,4,1) ,(1,-2,1), (-2,-1,1) (d) (2,-1,0) , (1,2,-3), (1,-3,2) (e) (5,1,-5) , (1,-2,-3), (-2,3,-4) (f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)arrow_forwardI don't understand 2 points in the solution for this problem. Can you please explain why? Thanks. 1. Why : {1, √2} is a basis for Q(√2) over Q then we conclude 2rs = 0 and r2 + 2s2 = 0 ??? 2. Why: [F : Q(√2) ] = 2arrow_forward10.Suppose that each of the vectors x(1), …, x(m) has n components, where n < m. Show that x(1), …, x(m) are linearly dependent. In each of Problems 11 and 12, determine whether the members of the given set of vectors are linearly independent for −∞ < t < ∞ . If they are linearly dependent, find the linear relation among them.arrow_forward
- for this problem, it cannot be assumed that A is diagonal. In particular, A2 = A does not imply A = 0 or A = I, and A2 = I does not imply A = ±I. Helpful notes attachedarrow_forwardFor part b) do we need to check whether the list (x, x, x/2) is also linearly independent? Since a basis of V is a list of vectors in V that is linearly independent and spans V and we know that span = (x, x, x/2) there is also the requirement of linear independence?arrow_forwardThis is under the subject of Linear Algebra and Vector Analysisarrow_forward
- Why is the given set of vectors not a basis for R^3? S={(1,2,-1),(1,1,1),(1,0,1)}arrow_forwardI need to solve this without using matrices. The components of a vector V in the basis B = (v1,v2) are (3,-2). Which are the components of the same vector in the basis C = (u1,u2), if v1 = 4u1-u2 and v2 = 4u1-3u2? Remember, no matrices.arrow_forwardFind the answer to the following subtraction problems by using vectors on the number line in conjunction with the missing addend approach. Draw an arrow from the subtrahend to the minuend 4 - 4arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage