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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
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
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
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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