alleryStart learning →A matrix A is INVERTIBLE if and only if
Adet(A) ≠ 0 (equivalently, A is full rank)
Btr(A) ≠ 0
CA is symmetric
Ddet(A) = 0
Answer & Solution
Correct answer: A. det(A) ≠ 0 (equivalently, A is full rank)
Non-zero determinant ⇔ full column rank ⇔ injective map ⇔ invertible.
Trace and symmetry do not characterise invertibility.
Keep practising Math for AI LA Probability
Browse all Math for AI LA Probability questions for Claude, or explore more Aifoundations topics.
Related questions
Conditional probability is defined asFor a Poisson(λ) random variable, the mean equals the variance and both equalEigenvalues λ of a square matrix A satisfyFor the standard NORMAL distribution N(0, 1), the mean and variance areBayes's rule allows you to computeA Binomial(n, p) random variable has mean and varianceFor two independent random variables X and YThe trace of a matrix A ∈ ℝ^(n×n), tr(A), is