x₁ - 5x₂ = ₁ X1 3x₁ + 2x₂ = b₂ i. b₁ = 1, b₂ = 4 ii. b₁ = -2, b₂ = 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
1.6 Question 9 and 15 please on paper. Thanks alot

Transcribed Image Text:1.
b₁ = 1,
b₂ = 0,
b₂
ii. b₁ = 0,
b₂ = 1,
b₂ = 1
iii. b₁ = -1,
b₂ = -1,
b₂ = 0
In Exercises 13-17, determine conditions on the bi's, if any, in order
to guarantee that the linear system is consistent.
13.
14. 6x₁4x₂ = b₁
x₁ + 3x₂ = b₁
-2x₁ + x₂ = b₂
3x₁ - 2x₂ = b₂
15.
16.
X₁ - 2x₂ + 5x3 = b₁
4x₁ - 5x₂ + 8x3 = b₂
-3x₁ + 3x₂ - 3x3 = b3
x₁2x₂x3 = b₁
-4x₁ + 5x₂ + 2x3 = b₂
-4x₁ + 7x₂ + 4x3 = b3
x₁ -
x₂ + 3x3 + 2x₁ = b₁
-2x₁ +
x₂ + 5x3 + x₁ = b₂
X2 X4
-3x₁ + 2x₂ + 2x3
x4 = b3
4x13x₂ + x3 + 3x4 = b4
17.
18. Consider the matrices

Transcribed Image Text:8.
7. 3x₁ + 5x₂ = b₁
x₂ + 2x₂ = b₂
x₁ + 2x₂ + 3x₂, = b₁
2x₁ + 5x₂ + 5x3 = b₂
3x₁ + 5x₂ + 8x3 = b₂
In Exercises 9-12, solve the linear systems. Using the given values for
the b's solve the systems together by reducing an appropriate aug-
mented matrix to reduced row echelon form.
9.
X₁ - 5x₂ = b₁
3x₁ + 2x₂ = b₂
ii. b₁ = -2, b₂ = 5
i. b₁ = 1, b₂ = 4
x3 = b₁
x₁ + 9x₂ - 2x3 = b₂
6x₁ + 4x₂ - 8x3 = b3
i. b₁ = 0, b₂ = 1, b3 = 0 ii. b₁ = -3, b₂ = 4, b3 = -5
10. -x₁ + 4x₂ +
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