111Problem 2. Let A =1-11111 113(a)(b)Find the QR decomposition of A. Hint: every entry of Q will be ±.What is QTQ?What is the dimension of the subspace V of R spanned by the first threecolumns of A?(d)Let wthe fourth column of A. Find the orthogonal projection of wonto V.What is the orthogonal projection of w onto V-?

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Answered: 1 3 -1 1 Problem 2. Let A 1 0 1 1 1 1 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let f(x, y) = xy² and r(t) = (¹/1²,t³). Calculate Vf. (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) Vf= Calculate r' (t). (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) r' (t) = Use the Chain Rule for Paths to evaluateƒ(r(t)) at t = 1.5. (Use decimal notation. Give your answer to three decimal places.) d dt - ƒ(r(1.5)) = = Use the Chain Rule for Paths to evaluate ƒ(r(t)) at t = -1.7. (Use decimal notation. Give your answer to three decimal places.) d dt d f(r(-1.7)) =

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1 3 -1 1 Problem 2. Let A 1 0 1 1 1 1 1 3 (a) (b) Find the QR decomposition of A. Hint: every entry of Q will be +;. What is QTQ? What is the dimension of the subspace V of R' spanned by the first three columns of A?