Common Core · High school
HSA-REI.C.8
High school — Represent a system of linear equations as a single matrix equation in a vector variable.
A note on this mapping: HSA-REI.C.8 is a (+) standard — beyond the college- and career-ready threshold, i.e. precalculus rather than Algebra II.
The 2 skills that cover it
- Row Reduction & Gaussian EliminationThe one procedure the whole subject leans on: apply a row operation and say what it did, clear a column below a pivot, drive a matrix all the way to reduced row echelon form, count the pivots, and recognise when a matrix is not in that form yet and which rule it breaks.Read the lesson →
- Linear Systems in Matrix FormA system of equations rewritten as one matrix equation: build the augmented matrix, read a matrix back as a system, solve two and three unknowns by elimination, and decide from the reduced form whether there is one solution, none at all, or a whole line of them.Read the lesson →
What a student should be able to do
- Apply a row operation to a matrix and give the resulting entry, or name the operation that turned one matrix into another.
- Find the multiplier that clears an entry below a pivot, and carry out forward elimination.
- Reduce a matrix to reduced row echelon form.
- Count the pivots of a matrix and decide whether it is already in reduced row echelon form.
- Write a system as an augmented matrix, and read an augmented matrix back as a system.
- Solve a system of two or three equations by row reduction.
- Decide from a reduced matrix whether a system has one solution, no solution, or infinitely many.
- Describe an infinite solution set with a free variable, and find the value that makes a system inconsistent.