Technology for Matrices

Using Technology to Perform Matrix Operations

Why Use Technology?

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.

Entering a Matrix on CAS

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

Operations Available

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)`

Worked Example — Using \(T^n\)

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.

Checking Your Work

Always verify the order of the result matches \(m \times n\) expectations.
For transition matrices, check that state vector entries sum to the original total (conservation of population).
Use CAS to check hand calculations on lower-stakes parts of multi-step questions.

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.

Technology for Matrices

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