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7. Let E be the Euclidean space M22 (R) equipped with the inner product (A,B) = a₁,1b1,1 + a1,2b1,2 + a21b2,1 + a22b2.2- for Further, let a1,1 1,2 - (8 2). a2,1 2,2 where A = -(1 B = ;). W = {A € M₂2 (R): (A,X) = 0 and (A,Y)=0} *-(¹) -(19) X = Find the orthogonal projection of C on the orthogonal complement W, when c-(13) C= b₁,1 1,2 b2,1 2,2

7. Let E be the Euclidean space M22 (R) equipped with the inner product (A,B) = a₁,1b1,1 + a1,2b1,2 + a21b2,1 + a22b2.2- for Further, let a1,1 1,2 - (8 2). a2,1 2,2 where A = -(1 B = ;). W = {A € M₂2 (R): (A,X) = 0 and (A,Y)=0} *-(¹) -(19) X = Find the orthogonal projection of C on the orthogonal complement W, when c-(13) C= b₁,1 1,2 b2,1 2,2

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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7. Let E be the Euclidean space M22 (R) equipped with the inner product (A,B) = a₁.b₁,1 + a1,2b1,2 + a21b2,1 + a22b22- for Further, let ( where a1,1 1,2 a2,1 2,2 ). X = B = W = {A € M₂,2(R): (A,X) = 0 and (A,Y)=0} -1 20 (17¹), x-(²9) Y = 0 11 Find the orthogonal projection of C on the orthogonal complement W, when C= b₁,1 b12 b2,1 2,2 ( 12 - (1²) 34
Transcribed Image Text:7. Let E be the Euclidean space M22 (R) equipped with the inner product (A,B) = a₁.b₁,1 + a1,2b1,2 + a21b2,1 + a22b22- for Further, let ( where a1,1 1,2 a2,1 2,2 ). X = B = W = {A € M₂,2(R): (A,X) = 0 and (A,Y)=0} -1 20 (17¹), x-(²9) Y = 0 11 Find the orthogonal projection of C on the orthogonal complement W, when C= b₁,1 b12 b2,1 2,2 ( 12 - (1²) 34
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