Practice question · Multiple choice
Solving Ax = b by computing A⁻¹ then multiplying is mathematically correct and numerically discouraged. What is the objection?
Hints
- Computing A⁻¹ means solving Ax = e for each column of the identity. How many systems is that?
- Every arithmetic operation rounds. Which route performs more of them?
Show the answer
D. Both cost and accuracy: n systems instead of one, with more error
Why
The inverse costs n systems where you needed one, roughly three times the work, and every extra operation rounds. Both routes are exact on paper and only one is exact in floating point, which is why numpy.linalg.solve exists and calling inv first is the classic beginner's tell.
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.
- Match each operation to the job it does.
- 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.