Question

Write the system of equations with the given coefficient matrix and right-hand side vector. $$A=\left[\begin{array}{rrrr}1 & -1 & 2 & 3 \\1 & 1 & -2 & 6 \\3 & 1 & 4 & 2 \end{array}\right], \mathbf{b}=\left[\begin{array}{r}1 \\-1 \\2\end{array}\right].$$

Name: Problem 12, Chapter 2: Differential Equations and Linear Algebra
Uploaded: 2020-05-08T20:30:32-08:00
Duration: 1 min 48 s
Channel: Jack Chen
Description: Write the system of equations with the given coefficient matrix and right-hand side vector. A=[ 1 -1 2 3 1 1 -2 6 3 1 4 2 ], 𝐛=[ 1 -1 2 ].

   Write the system of equations with the given coefficient matrix and right-hand side vector.
$$A=\left[\begin{array}{rrrr}1 & -1 & 2 & 3 \\1 & 1 & -2 & 6 \\3 & 1 & 4 & 2 \end{array}\right], \mathbf{b}=\left[\begin{array}{r}1 \\-1 \\2\end{array}\right].$$

Differential Equations and Linear Algebra

Stephen W. Goode,… 4th Edition

Chapter 2, Problem 12

Instant Answer

Solved by Expert Jack Chen

05/08/2020

Step 1

The matrix A is a 3x4 matrix, which means we have 3 equations and 4 variables. The variables can be denoted as x, y, z, and w. Show more…

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Write the system of equations with the given coefficient matrix and right-hand side vector. $$A=\left[\begin{array}{rrrr}1 & -1 & 2 & 3 \\1 & 1 & -2 & 6 \\3 & 1 & 4 & 2 \end{array}\right], \mathbf{b}=\left[\begin{array}{r}1 \\-1 \\2\end{array}\right].$$

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Key Concepts

Right-hand Side Vector

A column vector that holds the constant terms from each equation in the system. It represents the outputs or targets that the linear combinations of the variables are set equal to, completing the formulation of the linear system.

Coefficient Matrix

A rectangular array that contains the coefficients of the variables from a system of linear equations. This matrix provides a compact representation of the system by focusing on the multipliers attached to the variables in each equation.

System of Linear Equations

A collection of linear equations involving the same set of variables. Each equation represents a linear combination of the variables equal to a constant. The system is solved by finding values for the variables that satisfy all equations at the same time.

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