Matrices Question Type¶

Students enter a 2D matrix of values.

Basic Syntax¶

[matrix]
answer = [[1, 2], [3, 4]];

Options¶

`answer` (required)¶

The correct matrix in 2D array format.

[matrix]
answer = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];  // Identity matrix

`rows`, `cols`¶

Expected matrix dimensions.

[matrix]
answer = [[1, 2, 3], [4, 5, 6]];
rows = 2;
cols = 3;

`tolerance`¶

Acceptable error for each element.

[matrix]
answer = [[1.5, 2.7], [3.1, 4.2]];
tolerance = 0.01;

Examples¶

Matrix Multiplication¶

$A = "[[1, 2], [3, 4]]";
$B = "[[5, 6], [7, 8]]";

Multiply the matrices:
`A = $A` and `B = $B`

[matrix]
answer = [[19, 22], [43, 50]];
rows = 2;
cols = 2;
tolerance = 0.01;

Augmented Matrix from System¶

Write the augmented matrix for the system:
`2x + 3y = 5`
`x - y = 2`

[matrix]
answer = [[2, 3, 5], [1, -1, 2]];
rows = 2;
cols = 3;

Identity Matrix¶

What is the 3×3 identity matrix?

[matrix]
answer = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];
rows = 3;
cols = 3;

Row-Reduced Echelon Form¶

Use row reduction to solve the system, then write the result in RREF.

Original: `[[1, 2, 3], [2, 1, 4]]`

[matrix]
answer = [[1, 0, 1.4], [0, 1, 0.8]];
rows = 2;
cols = 3;
tolerance = 0.01;

Grading¶

The system: 1. Parses the student's matrix input 2. Checks dimensions match (if specified) 3. Compares each element within tolerance 4. Returns Correct if all elements match, Incorrect otherwise

Display Format¶

Students enter matrices in row-by-row format, typically with a visual input grid:

[1.5] [2.3] [3.1]
[4.2] [5.6] [6.7]

Tips¶

Specify dimensions: Helps students understand expected output size
Set reasonable tolerance: Rounding errors accumulate in complex calculations
Provide context: Explain what the matrix represents (transformation, system, etc.)
Start with small matrices: 2×2 or 2×3 before larger systems