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Let pu: R³ → U be the orthogonal projection onto the subspace U = {(x, y, z) = R³: x-y-z=0}. Consider the linear varieties 5 = {(2, 1, 2) € R³¹ : { =8=⁰}, U' = {(x, y, z) R³:a-y-z=3}. x-1=0 Determine a linear variety S'CU' whose orthogonal projection onto U is S, i.e. such that pu (S')= S.

Let pu: R³ → U be the orthogonal projection onto the subspace U = {(x, y, z) = R³: x-y-z=0}. Consider the linear varieties 5 = {(2, 1, 2) € R³¹ : { =8=⁰}, U' = {(x, y, z) R³:a-y-z=3}. x-1=0 Determine a linear variety S'CU' whose orthogonal projection onto U is S, i.e. such that pu (S')= S.

Advanced Engineering Mathematics
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 pu: R³ → U be the orthogonal projection onto the subspace U = {(x, y, z) = R³: x-y-z=0}. Consider the linear varieties S = {(2,1, 2) € R³: {* =6=⁰}, U' = {(x, y, z) = R³: a-y-z=3}. x-y-z=0 x-1=0 Determine a linear variety S'CU' whose orthogonal projection onto U is S, i.e. such that pu (S') = S.
Transcribed Image Text:Let pu: R³ → U be the orthogonal projection onto the subspace U = {(x, y, z) = R³: x-y-z=0}. Consider the linear varieties S = {(2,1, 2) € R³: {* =6=⁰}, U' = {(x, y, z) = R³: a-y-z=3}. x-y-z=0 x-1=0 Determine a linear variety S'CU' whose orthogonal projection onto U is S, i.e. such that pu (S') = S.
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