PROBLEMS
For Problems 1-14, determine the component
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Differential Equations and Linear Algebra (4th Edition)
- From the system x' = -x + 5y og y' = -y show that the vector function (top of picture) is a solution of the system only if (bottom of picture) is true.arrow_forwardIf u = < 3 , 9 > and v = < -3, 1 >, find 1/3u - 2v. (this is a vector problem)arrow_forwardIn Problems 21–26, decompose v into two vectors v1 and v2 , where v1 is parallel to w, and v2 is orthogonal to w. 25. v = 3i + j, w = - 2i - jarrow_forward
- Question 1) Resolve the vector into its x- and y-components. 940N < 326° x= y= Round to whole numbers**arrow_forwardCan you help me find the unique vector described in problem 2?arrow_forwardFor the following three vectors, what is 2⋅C→⋅(2A→×B→) ?A→=3.00î+4.00ĵ-4.00k̂B→=-2.00î+2.00ĵ+2.00k̂C→=7.00î-9.00ĵarrow_forward
- In Problem,decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w. v = i - 3j, w = 4i - jarrow_forwardQuestion B.3 Consider the minimization problem M(p, y) = min x U(x) s.t. p1 · x1 + ... + pn · xn ≤ y where U : Rn → R is continuous. Prove that the function M(p, y) : Rn + × R+ → R is quasi-concave. [Hint: the subscript + means that all elements of a vector are non negative and at least one is strictly larger than zero.]arrow_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
- Find a basis for the intersection of the two planes T1 and T2 whose equations are T1 : x + 3y + 7z = 0 and T2: 2x + 6y + 15z = 0.arrow_forwardFind the coordinate vector of ?=2−4? relative to the basis ?={?1,?2} for ?1 where ?1=3+8?, ?2=1+?.arrow_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_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning