Question

Reduce the system of linear equations to upper triangular form and 2x+3y=5 Solve -y=-2+frac{2}{3}x

Forms of linear equations
ANSWERED
asked 2020-11-03
Reduce the system of linear equations to upper triangular form and
\(2x+3y=5\)
Solve
\(-y=-2+\frac{2}{3}x\)

Answers (1)

2020-11-04

We are going to use following elementary row operations:
\(\circ \text{Interchange i-th and j-th row:} R_i \leftrightarrow R_j\)
\(\circ \text{Multiply i-th row by scalar } \alpha\ R_i \leftrightarrow \alpha \cdot R_i\)
\(\text{Add } \alpha \text{ times i-th row to j-th row: } R_j \rightarrow R_j+\alpha \cdot R_i\)
\(\begin{bmatrix} 2 &3 & 5\\ -\frac{2}{3} & -1 & -2 \end{bmatrix} R_2\rightarrow3 \cdot R_2 \begin{bmatrix} 2 &3 & 5\\ -2 & -3 & -6 \end{bmatrix}\)
\(R_2 \rightarrow R_2+R_1 \begin{bmatrix} 2 &3 & 5\\ 0 & 0 & -1 \end{bmatrix}\)
The second equation is 0=-1 . Contradiction , so the system doesnt have a solution.

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