Matrix — Precalculus, what it means and where it is taught
A rectangular array of numbers, described by its rows then columns.
Taught in Precalculus.
Where it is taught
What uses it later
This idea is needed for:
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
- Identity matrix — The square matrix with ones down the diagonal; it leaves everything unchanged.
- Determinant — A single number computed from a square matrix; zero means it has no inverse.
Practise this idea
6 questions in the course bank use Matrix, in Matrices & Systems.
Problem 1
Give the dimensions of a matrix with 3 rows and 5 columns, in the form rows x columns.
Worked answer
3x5
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Problem 2
Can a 2 × 3 matrix multiply a 2 × 4 matrix?
- No — the inside numbers disagree
- Yes, giving 2 × 4
- Yes, giving 3 × 2
- Only if both are square
Worked answer
No — the inside numbers disagree
3 ≠ 2, so the rows and columns cannot pair up
Problem 3
A 2 × 3 matrix multiplies a 3 × 4 matrix. Give the dimensions of the result, as rows x columns.
Worked answer
2x4
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Problem 4
Is AB always equal to BA for matrices?
- No
- Yes
- Only for 2 × 2
- Only when both are invertible
Worked answer
No
Matrix multiplication depends on order
Often only one of the two products even exists
Problem 5
A 2 × 2 matrix has determinant 0. How many inverses does it have?
Worked answer
0
Zero determinant means no inverse exists
Problem 6
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