Practice question · Put in order
Order the stages of solving a linear system by Gaussian elimination.
- Continue column by column until the matrix is in row echelon form
- Back-substitute from the bottom row upward to find the solution
- Use row operations to clear the entries below the first pivot
- Write the augmented matrix of the system
- Inspect for an inconsistent row or for rows of all zeros
Hints
- Elimination comes first and substitution last, the triangular shape must exist before you can climb it.
- You need to know which of the three cases you are in before reading off an answer.
Show the answer
- Write the augmented matrix of the system
- Use row operations to clear the entries below the first pivot
- Continue column by column until the matrix is in row echelon form
- Inspect for an inconsistent row or for rows of all zeros
- Back-substitute from the bottom row upward to find the solution
Why
Set up the augmented matrix, eliminate downward to reach echelon form, diagnose the case, then back-substitute. Reading off a solution before checking for an inconsistent row is how students end up 'solving' systems that have no solution.
Practise Systems of Linear Equations
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More questions on Systems of Linear Equations
- A system of two linear equations in two unknowns has exactly one solution, no solution, or infinitely many -…
- Sort each manipulation by whether it is a legitimate row operation on a system.
- Three equations in three unknowns can have no solution even when no two of them contradict each other. How?
- Select every system below that is INCONSISTENT, meaning it has no solution.
- A consistent linear system with more unknowns than equations always has infinitely many solutions.