Practice question · Select all that apply
Which properties of a matrix survive every elementary row operation?
Hints
- Row reduction is used to solve , so whatever it does, it cannot disturb the solutions.
- Ask what a row swap does to the sign of a determinant.
Show the answer
- B. The solution set of
- C. The rank
- D. The row space
Why
Rank, row space and the null space are what row reduction is built to preserve, which is why solving by elimination is legitimate. The determinant is not: a row swap flips its sign and scaling a row by multiplies it by .
Practise Systems of Linear Equations and Gaussian Elimination
The app has 8 more questions on this lesson, and keeps your place in the course. Physics I is free to start.
More questions on Systems of Linear Equations and Gaussian Elimination
- Order the steps of Gaussian elimination.
- While solving a linear system you reach the row 0 0 | 5. What has the algebra just told you?
- A system of 3 equations in 3 unknowns always has exactly one solution.
- Gaussian elimination changes a system’s appearance completely while leaving its solutions untouched. What…