Let N(A) A = span = [⁰ Гоо о ⁰1. 0 Find a spanning set for the null space of A. 2 6 -2 2
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- Send correct answer pleaseQ3) Let L = Z* and |x ||= max {|x1 - x3l, x2l, 15x,1} Vx = (x1, X2, X3, X4) E Z*. Is (Z*, ) is a normed space?5) Let X and Y be normed spaces. Suppose T:X → Y be a closed linear operator. Let (xn) be a sequence in X such that xn → x €X and Txn → y € Y. Show that y = Tx. Notice: Since X and Y are not given as Banach spaces, you can not use Closed Graph Theorem directly.
- 17. Show that if X is a normed linear space and if X is separable, then so is X/M.8. (. you list are all different from each other and from P7. ) List four vector spaces that are isomorphic to P7. Please make sure that the vector spacesLet {V₁,..., Vn} be a spanning set for an inner product space V. Suppose that x and y are such that (x, vk) = (y, vk) for all k. Prove that x = y. . Please prove this from definitions and do not refer to previous review, hw, or gw problems (you will lose points if you do so). If you use a theorem or property from the text (that has been proved), please refer to which one.
- 1. Find the union C1 U C2 and the intersection C1n C2 of the two sets C1 and C2, where (a) C1 = {0, 1, 2, }, C2 = {2,3, 4}. (b) C1= {x:0 < x <2}, C2= {x :112. If the null space of 0 10 0 0 1 a3. az, and if the null space of A consists of all multiples of then the value of a2 is: [a3] Page 4of3 4321Let (X, τ1) be any topological space and (X, τf ) be the finite complement topological space.Show that the space (X, τ1) is a T1−space if and only if τf ⊆ τ1.Prove that (Co0, 11·11,) is not a Banach Space for any 11. Check that the following functions on R² are norms: 1/p a) | (1,72) ||,= (1z1P" + \#a!P), 1spwrite in full senRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,