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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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