Mathematics•Hard

Matrix Operations

Mathematics challenge: Linear algebra underpins computer graphics, machine learning, physics simulations, and more. Master matrix operations.

Scenario

Work through a series of matrix calculations covering multiplication, determinants, and eigenvalues.

Question 1

Multiply: A = [[1,2],[3,4]], B = [[2,0],[1,3]]. What is entry (1,1) of AB (top-left)?

Question 2

What is the determinant of A = [[3,1],[2,4]]?

Question 3

For matrix A = [[2,0],[0,3]], what are the eigenvalues?

λ = 2 and λ = 3λ = 5 onlyλ = 6 onlyλ = 1 and λ = 6

Question 4

A matrix is invertible (non-singular) if and only if its determinant is:

PositiveZeroNon-zeroGreater than 1

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