1- (a) (b) dx In the following problems write the given linear system in matrix form. = 3x - 5y dy = 4x+8y dt dx =x-y+z+t-1 dt dy = 2x+y-z- 3t² dt dz =x+y+z+t²-t+2 dt
1- (a) (b) dx In the following problems write the given linear system in matrix form. = 3x - 5y dy = 4x+8y dt dx =x-y+z+t-1 dt dy = 2x+y-z- 3t² dt dz =x+y+z+t²-t+2 dt
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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![**Problem Set: Writing Linear Systems in Matrix Form**
**Instructions:**
In the following problems, write the given linear system in matrix form.
---
**Problem 1:**
(a)
\[
\frac{dx}{dt} = 3x - 5y \\
\frac{dy}{dt} = 4x + 8y
\]
(b)
\[
\frac{dx}{dt} = x - y + z + t - 1 \\
\frac{dy}{dt} = 2x + y - z - 3t^2 \\
\frac{dz}{dt} = x + y + z + t^2 - t + 2
\]
---
**Guidance:**
- Identify the coefficients of each variable in the linear equations.
- Write the system in the form of \(\frac{d\mathbf{x}}{dt} = A\mathbf{x} + \mathbf{b}\), where \(A\) is the matrix of coefficients, \(\mathbf{x}\) is the vector of variables, and \(\mathbf{b}\) is the vector representing constant terms (if any).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a46b8d2-68f8-4ff5-85d9-0145753bf32f%2F4a789331-9904-40b6-8535-3fb0b2b032f3%2F5ainhl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Set: Writing Linear Systems in Matrix Form**
**Instructions:**
In the following problems, write the given linear system in matrix form.
---
**Problem 1:**
(a)
\[
\frac{dx}{dt} = 3x - 5y \\
\frac{dy}{dt} = 4x + 8y
\]
(b)
\[
\frac{dx}{dt} = x - y + z + t - 1 \\
\frac{dy}{dt} = 2x + y - z - 3t^2 \\
\frac{dz}{dt} = x + y + z + t^2 - t + 2
\]
---
**Guidance:**
- Identify the coefficients of each variable in the linear equations.
- Write the system in the form of \(\frac{d\mathbf{x}}{dt} = A\mathbf{x} + \mathbf{b}\), where \(A\) is the matrix of coefficients, \(\mathbf{x}\) is the vector of variables, and \(\mathbf{b}\) is the vector representing constant terms (if any).
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