Let p = |0, P2 =| 2, n, and n =|1 Let Hj be the hyperplane in R³ passing through the point p, and having normal vector n¡, and let H, be the hyperplane in R³ passing through the point p, and having normal vector ng. (a) Find linear functionals fi and f2, and real numbers dį and dą such that Hị = [f1,di] and H2 = [f2, da]. (b) Give an explicit description of H1 n Hz by a formula that shows how to generate all points in Hj n Hq.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let p = |0, P2 =| 2, n,
and n =|1
Let Hj be the
hyperplane in R³ passing through the point p, and having normal vector n¡, and let H, be the
hyperplane in R³ passing through the point p, and having normal vector ng.
(a) Find linear functionals fi and f2, and real numbers dį and dą such that Hị = [f1,di] and
H2 = [f2, da].
(b) Give an explicit description of H1 n Hz by a formula that shows how to generate all points
in Hj n Hq.
Transcribed Image Text:Let p = |0, P2 =| 2, n, and n =|1 Let Hj be the hyperplane in R³ passing through the point p, and having normal vector n¡, and let H, be the hyperplane in R³ passing through the point p, and having normal vector ng. (a) Find linear functionals fi and f2, and real numbers dį and dą such that Hị = [f1,di] and H2 = [f2, da]. (b) Give an explicit description of H1 n Hz by a formula that shows how to generate all points in Hj n Hq.
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