17 12 7 -24 11. Let u 11 and u = 34 3 5 19 2 1 3 17 12 -1 3 17 12 1 3 8 7 -2 -24 11 34 7 -2 -24 11 19 34 1 5 Let A = Hint: 3 2 0 -2 -10 -10 5 19 5 2 6 16 2 1 1 11 1 1 11 (a) Find the general solution to the matrix equation Ax = 0 for x = X2 Give your X3 X4 solution in (parametric) vector form. (b) Do the columns of matrix A span R*? Briefly state why or why not. (c) Find a particular (a specific) non-trivial solution to the vector equation Xu, + x2u2 + x3uz + x4u4 = 0 (d) Is the set of vectors {u, uz, u3, u4} linearly independent or linearly dependent? Briefly support your answer. (e) Is u, in the span of {u, uz, u4}? If yes, write u, as a linear combination of u, uz, and U4. If no, or if it is not possible to say, state why.
17 12 7 -24 11. Let u 11 and u = 34 3 5 19 2 1 3 17 12 -1 3 17 12 1 3 8 7 -2 -24 11 34 7 -2 -24 11 19 34 1 5 Let A = Hint: 3 2 0 -2 -10 -10 5 19 5 2 6 16 2 1 1 11 1 1 11 (a) Find the general solution to the matrix equation Ax = 0 for x = X2 Give your X3 X4 solution in (parametric) vector form. (b) Do the columns of matrix A span R*? Briefly state why or why not. (c) Find a particular (a specific) non-trivial solution to the vector equation Xu, + x2u2 + x3uz + x4u4 = 0 (d) Is the set of vectors {u, uz, u3, u4} linearly independent or linearly dependent? Briefly support your answer. (e) Is u, in the span of {u, uz, u4}? If yes, write u, as a linear combination of u, uz, and U4. If no, or if it is not possible to say, state why.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:17
12
7
11. Let u:
3
-24
Uz =
19
11
and u =
34
5
2
1
3
17
12
-1
3
17
12
1
3
8
7 -2 -24 11
34
7 -2 -24 11
1
5
Let A =
3
Hint:
3
2
0 -2
5
19
19 34
2
6
16
2
1
1
11
2
1
1
11
– 10 -10
(a) Find the general solution to the matrix equation Ax = 0 for x =
X2
Give your
X3
X4
solution in (parametric) vector form.
(b) Do the columns of matrix A span R*? Briefly state why or why not.
(c) Find a particular (a specific) non-trivial solution to the vector equation
Xu, + x2U2 + X3uz + x4u4 = 0
(d) Is the set of vectors {u1, uz, uz, u4} linearly independent or linearly dependent? Briefly
support your answer.
(e) Is u, in the span of {u1, uz, u4}? If yes, write u, as a linear combination of u, uz, and
U4. If no, or if it is not possible to say, state why.
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