Determinant — Precalculus, what it means and where it is taught
A single number computed from a square matrix; zero means it has no inverse.
Taught in Precalculus.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Matrix — A rectangular array of numbers, described by its rows then columns.
Practise this idea
7 questions in the course bank use Determinant, in Matrices & Systems.
Problem 1
Find the determinant of [3124].
Worked answer
10
3(4)-1(2) = 12-2 = 10
Problem 2
Find the determinant of [2613].
Worked answer
0
2(3)-6(1) = 6-6 = 0
Problem 3
A 2 × 2 matrix has determinant 0. How many inverses does it have?
Worked answer
0
Zero determinant means no inverse exists
Problem 4
For [4726], find the determinant.
Worked answer
10
4(6)-7(2) = 24-14 = 10
Problem 5
For the system 2x+3y=7, 4x+6y=1, find the determinant of the coefficient matrix.
Worked answer
0
2(6)-3(4) = 0
So there is no unique solution
Problem 6
A system has coefficient determinant 0 and the equations are not multiples of each other. How many solutions?
- None
- Exactly one
- Infinitely many
- Two
Worked answer
None
The lines are parallel and distinct
Parallel lines never meet
Problem 7
Find k so that [k436] has no inverse.
Worked answer
2
6k-12 = 0
k = 2