Practice question · Match the pairs
Match each operation to the job it does.
- Matrix-vector product
- Matrix product
- Determinant
- Adjacency matrix
- Encodes which nodes of a network are connected
- Gives the area scaling factor of a transformation
- Composes two transformations into one
- Applies one transformation to one point
Hints
- Two entries are operations, two are objects that carry information.
- One number summarises what a whole transformation does to area.
Show the answer
- Matrix-vector product → Applies one transformation to one point
- Matrix product → Composes two transformations into one
- Determinant → Gives the area scaling factor of a transformation
- Adjacency matrix → Encodes which nodes of a network are connected
Why
These four cover most of the unit's applications: transform a point, chain transformations, measure the distortion, and encode a network. Every application in the lesson is one of these used on different data, the abstraction-and-reuse message of the whole unit.
Practise Applications of Matrices and Vectors
The app has 4 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.
More questions on Applications of Matrices and Vectors
- Writing a system as Ax = b lets you solve it as x = A⁻¹b - but numerical software almost never computes the…
- Order the stages of attacking a real problem with linear algebra.
- A three-node network has adjacency matrix with rows (0, 1, 1), (1, 0, 1) and (1, 1, 0). The entry in row 1,…
- The matrix with rows (2, 0) and (0, 2) is applied to the plane. By what factor does it multiply areas?
- Rotation by 90 degrees is the matrix with rows (0, -1) and (1, 0). Apply it to the point (3, 1). What is the…
- Sort each object by how it is naturally represented.
- Complete the interpretation of adjacency matrix powers.
- Solving Ax = b by computing A⁻¹ then multiplying is mathematically correct and numerically discouraged. What…