(d) Find an orthonormal basis for V = im(A). (Hint: If you find that the numbers aren't working out cleanly and that bothers you, try starting with a different basis.) (e) Find the projection of = onto V.

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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Please answer d and e.

Consider the vectors v1
--
0.
and v3
0 in R3.
2
(a) Are v1, v2, and v3 linearly independent?
(b) Find bases for the image and kernel of the matrix
1
1
A =
1
1
1
-1 2
|
(c) What is the dimension of the subspace V = im(A) in R³?
(d) Find an orthonormal basis for V = im(A). (Hint: If you find that
the numbers aren't working out cleanly and that bothers you, try
starting with a different basis.)
(e) Find the projection of =
onto V.
Transcribed Image Text:Consider the vectors v1 -- 0. and v3 0 in R3. 2 (a) Are v1, v2, and v3 linearly independent? (b) Find bases for the image and kernel of the matrix 1 1 A = 1 1 1 -1 2 | (c) What is the dimension of the subspace V = im(A) in R³? (d) Find an orthonormal basis for V = im(A). (Hint: If you find that the numbers aren't working out cleanly and that bothers you, try starting with a different basis.) (e) Find the projection of = onto V.
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