Tx1 + 3x2 + 4x3 =7 (g) x1 + x2 + x3 + x4 = 0 %3D 2x1 + 3x2 – X3 – X4 = 2 3x1 + 2x2 + x3 + x4 = 5 3x1 + 6x2 – x3 – X4 = 4 %3D X1 – 2x2 = 3 2x1 + x2= 1 -5x1 + 8x2 = 4 (h) %3D (i) -2x1 + 2x2 + X3 = 4 3x1 + 2x2 + 2x3 = -x1 + 2x2 – x3 = 2 %3D %3D -3x1+ 8x2 + 5x3 = 17 () Xi + 2x2 – 3x3 + x4 = 1 -x1 - x2 + 4x3 – x4 = 6 -2x1 - – x4 = 1 - %3D 4x2 +7x3 (k) X1 + 3x2 + x3 + x4 = 3 %3D 2x1 – 2x2 + x3 + 2x4 = 8 X1-5x2 + X4 = 5 a list (1) X1 - 3x2 + X3 = 1 2x1 + x2 - X3= 2 free ollow, valent chelon ent. If X+4x2 - 2x3 = 1 8x2 + 2x3 5x1 6. Use Gauss-Jordan reduction to solve each of the following
Tx1 + 3x2 + 4x3 =7 (g) x1 + x2 + x3 + x4 = 0 %3D 2x1 + 3x2 – X3 – X4 = 2 3x1 + 2x2 + x3 + x4 = 5 3x1 + 6x2 – x3 – X4 = 4 %3D X1 – 2x2 = 3 2x1 + x2= 1 -5x1 + 8x2 = 4 (h) %3D (i) -2x1 + 2x2 + X3 = 4 3x1 + 2x2 + 2x3 = -x1 + 2x2 – x3 = 2 %3D %3D -3x1+ 8x2 + 5x3 = 17 () Xi + 2x2 – 3x3 + x4 = 1 -x1 - x2 + 4x3 – x4 = 6 -2x1 - – x4 = 1 - %3D 4x2 +7x3 (k) X1 + 3x2 + x3 + x4 = 3 %3D 2x1 – 2x2 + x3 + 2x4 = 8 X1-5x2 + X4 = 5 a list (1) X1 - 3x2 + X3 = 1 2x1 + x2 - X3= 2 free ollow, valent chelon ent. If X+4x2 - 2x3 = 1 8x2 + 2x3 5x1 6. Use Gauss-Jordan reduction to solve each of the following
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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Both pictures are part of the same question. I only need 5g and 5 k. Thank you
![of the lead Variables
a second 1ist of
variables.
5. For each of the systems of equations that follow,
use Gaussian elimination to obtain an equivalent
system whose coefficient matrix is in row echelon
form. Indicate whether the system is consistent. If
the system is consistent and involves no free vari-
ables, use back substitution to find the unique solu-
tion. If the system is consistent and there are free
variables, transform it to reduced row echelon form
and find all solutions.
X1 – 2x2 = 3
2x1 – x2 =9
(a)
(b)
2x1 – 3x2 = 5
-4x1 + 6x2 = 8
(c)
X1 + x2 =0
2x1 + 3x2 = 0
3x1 – 2x2 = 0
(d)
3x1 + 2x2 -
X3 = 4
X1 – 2x2 + 2x3 =
11x1 + 2x2 +
1
7.
X3 = 14
(e) 2x1 + 3x2 + x3 =1
tF
X1+ x2 x3 =3
tic
3x1 + 4x2 + 2x3 = 4
of
geo
FEB
14](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe55c0d8-c124-41b8-9441-1711c1d197bf%2F87a81373-82fb-47e9-8e84-41fb8ac76eb6%2F92q7hg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:of the lead Variables
a second 1ist of
variables.
5. For each of the systems of equations that follow,
use Gaussian elimination to obtain an equivalent
system whose coefficient matrix is in row echelon
form. Indicate whether the system is consistent. If
the system is consistent and involves no free vari-
ables, use back substitution to find the unique solu-
tion. If the system is consistent and there are free
variables, transform it to reduced row echelon form
and find all solutions.
X1 – 2x2 = 3
2x1 – x2 =9
(a)
(b)
2x1 – 3x2 = 5
-4x1 + 6x2 = 8
(c)
X1 + x2 =0
2x1 + 3x2 = 0
3x1 – 2x2 = 0
(d)
3x1 + 2x2 -
X3 = 4
X1 – 2x2 + 2x3 =
11x1 + 2x2 +
1
7.
X3 = 14
(e) 2x1 + 3x2 + x3 =1
tF
X1+ x2 x3 =3
tic
3x1 + 4x2 + 2x3 = 4
of
geo
FEB
14
![(f)
X1 - X2 + 2x3 = 4
2x1 + 3x2 - x3 = 1
7x1 + 3x2 + 4x3 = 7
(8)
X1 + x2 + x3 + x4 = 0
2x1 + 3x2 – x3 – x4 = 2
3x1 + 2x2 + x3 + x4 = 5
3x1 + 6x2 – x3 – X4 = 4
X1 – 2x2 = 3
2x1 + x2 = 1
(h)
-5x1 + 8x2 = 4
%3D
(i)
-x1 + 2x2 – x3 = 2
-2x1 + 2x2 + X3 = 4
3x1 + 2x2 + 2x3 = 5
-3x1 + 8x2 + 5x3 = 17
(j)
X1 + 2x2 - 3x3 + x4 = 1
-x1 - X2 + 4x3 – x4 = 6
-2x1 - 4x2 +7x3 – x4 = 1
(k)
X+3x2 + x3 + x4 = 3
2x1 - 2x2 + x3 + 2x4 = 8
X1 - 5x2
+ X4 = 5
ke a list
the free
(1)
X1-3x2 + X3 = 1
2x1 + x2 - X3 = 2
X1 + 4x2 – 2x3 = 1
5x1 - 8x2 + 2x3 = 5
at follow,
equivalent
w echelon
nsistent. If
o free vari-
anique solu-
еге агe free
6. Use Gauss-Jordan reduction to solve each of the
following systems:
Se
(a)
X1 + x2 = -1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe55c0d8-c124-41b8-9441-1711c1d197bf%2F87a81373-82fb-47e9-8e84-41fb8ac76eb6%2F5w9p2w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(f)
X1 - X2 + 2x3 = 4
2x1 + 3x2 - x3 = 1
7x1 + 3x2 + 4x3 = 7
(8)
X1 + x2 + x3 + x4 = 0
2x1 + 3x2 – x3 – x4 = 2
3x1 + 2x2 + x3 + x4 = 5
3x1 + 6x2 – x3 – X4 = 4
X1 – 2x2 = 3
2x1 + x2 = 1
(h)
-5x1 + 8x2 = 4
%3D
(i)
-x1 + 2x2 – x3 = 2
-2x1 + 2x2 + X3 = 4
3x1 + 2x2 + 2x3 = 5
-3x1 + 8x2 + 5x3 = 17
(j)
X1 + 2x2 - 3x3 + x4 = 1
-x1 - X2 + 4x3 – x4 = 6
-2x1 - 4x2 +7x3 – x4 = 1
(k)
X+3x2 + x3 + x4 = 3
2x1 - 2x2 + x3 + 2x4 = 8
X1 - 5x2
+ X4 = 5
ke a list
the free
(1)
X1-3x2 + X3 = 1
2x1 + x2 - X3 = 2
X1 + 4x2 – 2x3 = 1
5x1 - 8x2 + 2x3 = 5
at follow,
equivalent
w echelon
nsistent. If
o free vari-
anique solu-
еге агe free
6. Use Gauss-Jordan reduction to solve each of the
following systems:
Se
(a)
X1 + x2 = -1
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