An augmented matrix is a tool used to depict a system of linear equations. To solve these equations, one must execute basic row operations until the matrix is transformed into a row-echelon form or reduced row-echelon form. Once this form is achieved, the solutions can be interpreted directly from the final matrix. These solutions correspond to the variables in the initial equations.
| Topic | Problem | Solution |
|---|---|---|
| None | \( \begin{array}{c}3 x-y+z+7 w=13 \\ -2 x+y-z-3 w… | 1. Eliminate 'y' by adding Eq. (1) and Eq. (2): \\ \(x + 4w = 4\) |
| None | Write the augmented matrix of the following syste… | The given system of equations is: \[\begin{align*} -2x + y - 3 &= 0 \\ x - 5y + 6 &= 0 \end{align*… |
| None | Use Gauss-Jordan elimination to solve the followi… | First, we write the system of equations in augmented matrix form. The augmented matrix is: \[\begin… |
| None | Using the given matrix in reduced row echelon for… | The given matrix is in reduced row echelon form. This form corresponds to the system of linear equa… |
| None | Determine the solution to the given system of lin… | Create an augmented matrix from the given system of equations. The augmented matrix is a matrix tha… |
| None | Determine the solution to the given system of lin… | First, we write the system of equations as an augmented matrix: \[\begin{pmatrix} -2 & 7 & -8 & 30 … |
| None | (B) \[ \left\{\begin{array}{l} 2 x-3 y-z=0 \\ -2 … | \(\left\{\begin{array}{l} 2x-3y-z=0 \\ -2x+y+2z=-9 \\ 4x+2y+z=1 \end{array}\right.\) |
| None | 2. Consider the system of linear equations \[ \be… | The system of linear equations can be written in matrix form as follows: \[\begin{array}{ccc|c} 0 &… |
| None | 2. Consider the system of linear equations \[ \be… | Given the system of linear equations: \[\begin{array}{r} 2 y+3 z=0 \\ x+2 y+z=0 \\ -2 x-2 y+z=0 \en… |
| None | Use the Gauss-Jordan method to solve the system o… | We are given the system of equations: \[\begin{aligned} x+y-3 z & =-15 \\ 3 x-3 y+2 z & =7 \\ x+3 y… |
| None | Use the Gauss-Jordan method to solve the followin… | Represent the system of equations as an augmented matrix: \[\begin{array}{cc|c} 1 & 1 & 8 \\ 3 & 2 … |
| None | What is the augmented matrix of the following sys… | The augmented matrix is a matrix that is obtained from a system of linear equations. Each row of th… |
| None | What is the augmented matrix of the following sys… | The augmented matrix of a system of linear equations is a matrix that includes the coefficients of … |
| None | An animal feed to be mixed from soybean meal and … | Define the problem as a linear programming problem. The objective is to minimize the cost of the an… |
| None | Encontre a reta, interseção dos planos \[ \begin{… | A interseção de dois planos é uma linha. Podemos encontrar a equação desta linha resolvendo o siste… |
| None | Solve the system. If there is no solution or if t… | Represent the system of equations in matrix form. |
| None | Use Gaussian elimination to find the complete sol… | We start by writing the system of equations in augmented matrix form: \[\begin{bmatrix} 5 & 12 & 5 … |
| None | 3. Determine whether the system of equations has … | The system of equations is a linear system with three variables. To determine whether the system ha… |
| None | Solve the system. If there is no solution or if t… | We are given a system of linear equations with three variables. The system is as follows: \[\begin{… |
| None | (a) \[ \left[\begin{array}{lll:l} 1 & 0 & 4 & 4 \… | The given matrix is in row-echelon form. The last row of the matrix represents the equation 0x + 0y… |