On a TI-84 Plus CE
- Enter a matrix with 2nd → MATRX → EDIT. Determinant: det([A]); inverse: [A] then the x⁻¹ key.
- Solve A x = b by computing [A]⁻¹[b].
Tip: If det(A) = 0 there is no unique solution - the system has no solution or infinitely many.
Matrix operations and solving systems
Inverses, determinants and solving linear systems are quick and reliable on the GDC.
In short: Matrix operations on a GDC include adding, multiplying, finding the determinant and the inverse, and solving systems of equations. You enter each matrix in the matrix menu and combine them using the names you gave them. Check that the dimensions match before multiplying, and use the inverse or row reduction to solve linear systems.
When you'd use this
- Finding the inverse or determinant of a matrix quickly, without expanding by hand.
- Solving a linear system written in matrix form, Ax = b.
- Multiplying matrices that are too large to multiply reliably by hand.
- Checking a matrix calculation you did algebraically.
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | Enter a matrix with 2nd → MATRX → EDIT. Determinant: det([A]); inverse: [A] then the x⁻¹ key. | Run-Matrix → MAT/VCT (F3) to enter a matrix; use Det and the x⁻¹ key. | Use the matrix template (or menu → Matrix & Vector). det(), and ^-1 for the inverse. |
On a Casio fx-CG50 and fx-CG100
- Run-Matrix → MAT/VCT (F3) to enter a matrix; use Det and the x⁻¹ key.
- Solve A x = b by computing [A]⁻¹[b].
Tip: If det(A) = 0 there is no unique solution - the system has no solution or infinitely many.
On a TI-Nspire CX
- Use the matrix template (or menu → Matrix & Vector). det(), and ^-1 for the inverse.
- Solve A x = b by computing [A]⁻¹[b].
Tip: If det(A) = 0 there is no unique solution - the system has no solution or infinitely many.
Related guides
Try it yourself
Here's a real IB-style question that uses exactly this technique.
Medium
Calculator
Paper 2
[4 marks]
Given A = [[2, 1], [1, 3]] and b = [5, 10], find A⁻¹ and use it to solve Ax = b.
x = 1, y = 3
Mark it
Correct
4 / 4 marks
Worked solution & mark scheme:
M1 Find A⁻¹
M1 Compute A⁻¹b
A1 x = 1, y = 3
Common questions
When would I need to do matrix operations and solve systems in IB Maths?
Inverses, determinants and solving linear systems are quick and reliable on the GDC. Finding the inverse or determinant of a matrix quickly, without expanding by hand. Solving a linear system written in matrix form, Ax = b.
How do I do matrix operations and solve systems on a TI-84 Plus CE?
1. Enter a matrix with 2nd → MATRX → EDIT. Determinant: det([A]); inverse: [A] then the x⁻¹ key. 2. Solve A x = b by computing [A]⁻¹[b].
How do I do matrix operations and solve systems on a Casio fx-CG50 and fx-CG100?
1. Run-Matrix → MAT/VCT (F3) to enter a matrix; use Det and the x⁻¹ key. 2. Solve A x = b by computing [A]⁻¹[b].
How do I do matrix operations and solve systems on a TI-Nspire CX?
1. Use the matrix template (or menu → Matrix & Vector). det(), and ^-1 for the inverse. 2. Solve A x = b by computing [A]⁻¹[b].
What should I watch out for when I do matrix operations and solve systems?
If det(A) = 0 there is no unique solution - the system has no solution or infinitely many.
How are marks awarded when I do matrix operations and solve systems in an IB exam?
In the worked example on this page (4 marks, Paper 2), the marks are: M1: Find A⁻¹; M1: Compute A⁻¹b; A1: x = 1, y = 3.
Practise with your calculator
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.