Math  /  Algebra

Question1\checkmark 1 2\checkmark 2
An augmented matrix is given. Determine the number of solutions to the corresponding systen [100401060010]\left[\begin{array}{ccc|c} 1 & 0 & 0 & -4 \\ 0 & 1 & 0 & 6 \\ 0 & 0 & 1 & 0 \end{array}\right] The system has one solution. The system has no solution. The system has infinitely many solutions.

Studdy Solution

STEP 1

1. The augmented matrix represents a system of linear equations.
2. The matrix is in row-echelon form or reduced row-echelon form.
3. Each row of the matrix corresponds to an equation in the system.
4. The last column of the matrix represents the constants on the right-hand side of the equations.

STEP 2

1. Interpret the augmented matrix.
2. Determine the type of solution based on the matrix form.

STEP 3

Interpret the augmented matrix:
The given matrix is:
[100401060010]\left[\begin{array}{ccc|c} 1 & 0 & 0 & -4 \\ 0 & 1 & 0 & 6 \\ 0 & 0 & 1 & 0 \end{array}\right]
This corresponds to the system of equations:
\begin{align*} x_1 &= -4, \\ x_2 &= 6, \\ x_3 &= 0. \end{align*}
Each row represents an equation with a single variable, indicating a unique solution for each variable.

STEP 4

Determine the type of solution:
Since each variable x1x_1, x2x_2, and x3x_3 has a unique solution, the system has exactly one solution.
The system has one solution.
The system has one solution.

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