Find the projection matrix P = aa/aa onto the line through each vector a. Verify in both cases that P2 = P. Multiply Pb in each case to compute the projection p. (a) a P = 9. [1.66667 If b 2, then p = Pb = 1.66667 12 1.66667 (b) a = P = If b 3, then p = Pb = 3

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 13CM
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Find the projection matrix P = aa/aa onto the line through each vector a. Verify
in both cases that P2 = P. Multiply Pb in each case to compute the projection p.
(a)
a
1
=
P
=
9.
"
If b=2, then p
2
(b) a =
[1.66667]
=
Pb = 1.66667
1.66667
P =
9.
If b
=
3, then
P
3
=
Pb
=
3
G
Transcribed Image Text:Find the projection matrix P = aa/aa onto the line through each vector a. Verify in both cases that P2 = P. Multiply Pb in each case to compute the projection p. (a) a 1 = P = 9. " If b=2, then p 2 (b) a = [1.66667] = Pb = 1.66667 1.66667 P = 9. If b = 3, then P 3 = Pb = 3 G
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