In each part find a linear system in the unknowns x1, x2, x3, …, that corresponds to the given a

step 1 From the given augmented matrix, we can write the following corresponding linear equations. 3x2

In each part find a linear system in the unknowns x1, x2,...

In each part find a linear system in the unknowns $x_{1}, x_{2}, x_{3}, \ldots,$ that corresponds to the given augmented matrix. $$\text { (a) }\left[\begin{array}{ccccc} 0 & 3 & -1 & -1 & -1 \\ 5 & 2 & 0 & -3 & -6 \end{array}\right]$$ $$\text { (b) }\left[\begin{array}{rrrrr} 3 & 0 & 1 & -4 & 3 \\ -4 & 0 & 4 & 1 & -3 \\ -1 & 3 & 0 & -2 & -9 \\ 0 & 0 & 0 & -1 & -2 \end{array}\right]$$

In each part find a linear system in the unknowns $x_{1}, x_{2}, x_{3}, \ldots,$ that corresponds to the given augmented matrix.
$$\text { (a) }\left[\begin{array}{ccccc} 0 & 3 & -1 & -1 & -1 \\ 5 & 2 & 0 & -3 & -6 \end{array}\right]$$
$$\text { (b) }\left[\begin{array}{rrrrr} 3 & 0 & 1 & -4 & 3 \\ -4 & 0 & 4 & 1 & -3 \\ -1 & 3 & 0 & -2 & -9 \\
0 & 0 & 0 & -1 & -2 \end{array}\right]$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Linear System

A linear system is a collection of one or more linear equations involving the same set of variables. Each equation is formed by a linear combination of these unknowns set equal to a constant. Solving a linear system means finding values for the unknowns that simultaneously satisfy all of the equations.

Augmented Matrix

An augmented matrix is a compact way to represent a linear system by writing the coefficients of the variables and the constants in a matrix. The columns up to a certain point represent the coefficients of the unknowns, while the last column represents the right?hand side constants. This format facilitates the use of matrix operations to solve the system.

Correspondence Between Rows and Equations

In an augmented matrix, each row corresponds to a single equation in the linear system. The entries in the row are interpreted as the coefficients of the respective unknowns, and the final entry is the constant term of the equation. This direct correspondence allows one to easily convert between the matrix form and the explicit equation form of the problem.

Transcript

Please give Ace some feedback