2. Let 0 1 -1 2 1 0 1 -1 2 --()-) 1 1 5 0 -2 1 A = 2 1 5 1 0 1 1 2 В 1 0 6 1 9 -3 8 (a) Show that A and B are not row-equivalent. (b) Compute the values of rank(A) and rank(B). (c) Compute the general solution for each of the SLES Ax=0 and Bx = 0. (d) Find a solution of the SLE Bx = 0 that is not contained in the solution set of Ax = 0. (e) Is the SLE Ax = b consistent for every b e R³? Is the SLE Bx = b consistent for every beR? In the affirmative case, justify your answer. In the negative case, find a vector BER³ such that the SLE is inconsistent.

2. Let 0 1 -1 2 1 0 1 -1 2 --()-) 1 1 5 0 -2 1 A = 2 1 5 1 0 1 1 2 В 1 0 6 1 9 -3 8 (a) Show that A and B are not row-equivalent. (b) Compute the values of rank(A) and rank(B). (c) Compute the general solution for each of the SLES Ax=0 and Bx = 0. (d) Find a solution of the SLE Bx = 0 that is not contained in the solution set of Ax = 0. (e) Is the SLE Ax = b consistent for every b e R³? Is the SLE Bx = b consistent for every beR? In the affirmative case, justify your answer. In the negative case, find a vector BER³ such that the SLE is inconsistent.

Name: 2. Let10 1 -1 21 0 1 -1 2A =1 51 0B=2 1 51 00 -2 11 16 1 9 -3 8(a) Sh
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Description: 2. Let10 1 -1 21 0 1 -1 2A =1 51 0B=2 1 51 00 -2 11 16 1 9 -3 8(a) Show that A and B are not row-equivalent.(b) Compute the values of rank(A) and rank(B).(c) Compute the general solution for each of the SLES Ax= 0 and Bx = 0.(d) Find a solution of t

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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Question

2. Let
1
0 1 -1 2
1 0 1 -1 2
A =
1 5
1 0
B=
2 1 5
1 0
0 -2 1
1 1
6 1 9 -3 8
(a) Show that A and B are not row-equivalent.
(b) Compute the values of rank(A) and rank(B).
(c) Compute the general solution for each of the SLES Ax= 0 and Bx = 0.
(d) Find a solution of the SLE Bx =0 that is not contained in the solution set of Ax = 0.
(e) Is the SLE Ax = b consistent for every b E R?? Is the SLE Bx = b consistent for every
b ER³? In the affirmative case, justify your answer. In the negative case, find a vector
be R³ such that the SLE is inconsistent.

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