Matrices larger than \$2 \times 2$ are tedious to multiply by hand. CAS calculators (TI-Nspire, Casio ClassPad) perform operations instantly and accurately, freeing mental effort for interpretation.
TI-Nspire CX:
1. Press menu → Matrix & Vector → Create → Matrix
2. Enter the number of rows and columns
3. Type each entry, pressing tab to move between cells
Casio ClassPad:
1. Open the Main application
2. Tap Math keyboard → matrix template
3. Fill in dimensions and entries
| Operation | CAS input |
|---|---|
| Addition | matA + matB |
| Subtraction | matA - matB |
| Scalar multiplication | 3*matA |
| Matrix multiplication | matA * matB |
| Matrix power | matA^3 |
| Inverse | matA^(-1) or inverse(matA) |
| Determinant | det(matA) |
| Transpose | transpose(matA) |
Given the transition matrix $T$ and state vector $S_0$:
$$T = \begin{pmatrix} 0.85 & 0.10 \ 0.15 & 0.90 \end{pmatrix}, \quad S_0 = \begin{pmatrix} 500 \ 300 \end{pmatrix}$$
Find $S_5 = T^5 S_0$.
On CAS: define T and S0 as matrices, then compute T^5 * S0.
$$T^5 \approx \begin{pmatrix} 0.429 & 0.238 \ 0.571 & 0.762 \end{pmatrix}$$
$$S_5 \approx T^5 S_0 = \begin{pmatrix} 0.429(500)+0.238(300) \ 0.571(500)+0.762(300) \end{pmatrix} \approx \begin{pmatrix} 285.9 \ 514.1 \end{pmatrix}$$
Approximately 286 in State 1, 514 in State 2.
STUDY HINT: Practise entering matrices quickly on your CAS. In an exam, slow data entry under pressure loses time. Set up your notation: store $T$, $S_0$ as named matrices to avoid re-entry.
EXAM TIP: Show the matrix setup and the final answer. CAS output alone without supporting working may not attract full marks for method.
