Let A, b,, and b, be as defined below. 、目、 [1 2 -1 -2 2 0 2 3 -2 -3 4 0 A= |1 2 2 3 17 2 04 2 3 06 b, = 1 [3 4 -1 -2 4 2 { {1 (2 {1 (2 {3 0 }, 0 }, 4 }, 6 }, 4 , 2 -1 -2 -3 2 4 -2 2 3 4 3 -2 -1 2 } (b1, b2}= 7, 20 }, 1 } ( 10 , 17 4 { 1, 2, 1, 2, (a) Find all solutions (if any) to the homogeneous system of equations associated with Ax = b,. (b) Verify that x, = 3, x, = 2, x, =-1, x4 = -1, xs = 0, x, = 0 is a solution to Až = B,. (c) Find all solutions (if any) to the equation A = B,. %3D (d) Find all solutions (if any) to the homogeneous system of equations associated with Af = (e) Find all solutions (if any) to the equation A = b,. 2. %3D
Let A, b,, and b, be as defined below. 、目、 [1 2 -1 -2 2 0 2 3 -2 -3 4 0 A= |1 2 2 3 17 2 04 2 3 06 b, = 1 [3 4 -1 -2 4 2 { {1 (2 {1 (2 {3 0 }, 0 }, 4 }, 6 }, 4 , 2 -1 -2 -3 2 4 -2 2 3 4 3 -2 -1 2 } (b1, b2}= 7, 20 }, 1 } ( 10 , 17 4 { 1, 2, 1, 2, (a) Find all solutions (if any) to the homogeneous system of equations associated with Ax = b,. (b) Verify that x, = 3, x, = 2, x, =-1, x4 = -1, xs = 0, x, = 0 is a solution to Až = B,. (c) Find all solutions (if any) to the equation A = B,. %3D (d) Find all solutions (if any) to the homogeneous system of equations associated with Af = (e) Find all solutions (if any) to the equation A = b,. 2. %3D
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:Let A, b1, and b, be as defined below.
[1 2 -1
2 3 -2 -3 4 0
A= |1 2
-2 2 0
10
17
2
By =
2 0 4
3 0 6
1
2 3
2
3 4 -1 -2 4 2_
a=
{1
{2
{1
{2
{3, 4
0 },
0 },
4 },
6 },
2 }
-1
-2
2
3
-2 .
-3
4
2
2 ,
3
3
-1
-2,
4 ,
}
{b1, b2}=
{
{ 10 ,
{ 1,
}
20 },
1 }
17
4
7
1, 2 ,
(a) Find all solutions (if any) to the homogeneous system of equations associated with Af = b1.
(b) Verify that x1 = 3, x2 = 2, x3 =-1, x4 =-1, x5 = 0, x, = 0 is a solution to Af = b1.
(c) Find all solutions (if any) to the equation Ax = b,.
(d) Find all solutions (if any) to the homogeneous system of equations associated with Ax = b2.
(e) Find all solutions (if any) to the equation Ax = b2.
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