Determinants and Matrix Inverses
Master the key concepts of determinants, matrix inverses, and their properties.
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Questions Covered in This Set
10 cards to master
What is the formula for the determinant of a 2×2 matrix [[a, b], [c, d]]?
det(A) = ad - bc
What is the critical condition for a matrix to have an inverse?
The determinant must be non-zero (det(A) ≠ 0)
What is a singular matrix?
A matrix with determinant equal to zero that has no inverse
What is the formula for the inverse of a 2×2 matrix [[a, b], [c, d]]?
A⁻¹ = (1/det(A)) × [[d, -b], [-c, a]]
What does AA⁻¹ equal?
The identity matrix I
What is the relationship between det(AB) and det(A), det(B)?
det(AB) = det(A) × det(B)
What happens to the determinant when you transpose a matrix?
It stays the same: det(Aᵀ) = det(A)
What are the two main methods for finding inverses of 3×3 matrices?
Gauss-Jordan elimination and the adjugate method
Why does a matrix with linearly dependent rows have no inverse?
Because its determinant equals zero, making it singular
What is the relationship between det(A⁻¹) and det(A)?
det(A⁻¹) = 1/det(A)
