Question

For the following linear systems, put the augmented coefficient matrix into reduced row-echelon form, and use this to find the solution set: a) x₁+2x₂+x₃=1 (b) 3x₁+5x₂_x₃=14

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Answer 1

To put the augmented coefficient matrix into reduced row-echelon form, we'll use Gaussian elimination on the linear system x₁+2x₂+x₃=1. The reduced row-echelon form indicates there are infinitely many solutions.

Step-by-step explanation:

To put the augmented coefficient matrix into reduced row-echelon form, we will use a method called Gaussian elimination. Let's consider the first linear system:

a) x₁ + 2x₂ + x₃ = 1

To start, we can represent the system as an augmented matrix:

1 2 1 | 1

Next, we'll perform row operations to transform the matrix to its reduced row-echelon form:

1 2 1 | 1

0 -3 -1 | -2

0 0 0 | 0

The reduced row-echelon form of this matrix indicates that all variables are free variables, which means there are infinitely many solutions.