1. In each part of this question, you have been given a system of equations and the corresponding matrix taken to RREF. Write the general solution as a vector equation. • List the basic solutions. a. ● b. (x₁ - x₂ + 2x4 = 0 -x₁ + x₂ + 3x3 - 11x4 2x₁ - 2x₂ + 4x4 0 0 (-4x₁ + 4x₂ + 3x3 - 17x4 = 0 Lo - = 0 " [1 0 -1 0 2 01 0 1 -3 0 0 0 0 0 0 0 0 (3w+9y15z = 0 1 0 3 -14w + 33x - 75y - 62z = 0 0 1 -1 -4 -5w+ 14x29y - 31z = 0 0 0 (52w 164x + 320y + 396z = 0 Lo 0 0 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. In each part of this question, you have been given a system of equations and the corresponding matrix
taken to RREF.
Write the general solution as a vector equation.
• List the basic solutions.
a.
b.
(x₁ - x₂ + 2x4 = 0
[1
-X₁ + x₂ + 3x3 - 11x4
0
2x₁ - 2x₂ + 4x4
0
0
-4x₁ + 4x₂ + 3x3 - 17x4 = 0 Lo
-
= 0
"
-1 0
2 01
0 1 -3 0
0
0
0
0
0
00
(3w+9y15z = 0
1
0
-14w + 33x - 75y - 62z = 0
0 1
-5w+ 14x - 29y - 31z = 0
0
0
(52w 164x + 320y + 396z = 0 Lo
0
3
-1 -4
0
0
Transcribed Image Text:1. In each part of this question, you have been given a system of equations and the corresponding matrix taken to RREF. Write the general solution as a vector equation. • List the basic solutions. a. b. (x₁ - x₂ + 2x4 = 0 [1 -X₁ + x₂ + 3x3 - 11x4 0 2x₁ - 2x₂ + 4x4 0 0 -4x₁ + 4x₂ + 3x3 - 17x4 = 0 Lo - = 0 " -1 0 2 01 0 1 -3 0 0 0 0 0 0 00 (3w+9y15z = 0 1 0 -14w + 33x - 75y - 62z = 0 0 1 -5w+ 14x - 29y - 31z = 0 0 0 (52w 164x + 320y + 396z = 0 Lo 0 3 -1 -4 0 0
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