College · intermediate
Linear Algebra
Matrices, determinants, and linear systems by hand.
Skills
16 skills in 4 sections — fundamentals first, then more specific topics. Practice each until Mastery Score 100.
A.Vectors7 skills
- A.1 Vector Addition in the PlanePractice →Read vector addition from a head-to-tail diagram.
- A.2 Dot ProductPractice →Compute the dot product of R² or R³ vectors.
- A.3 Linear Combinations of VectorsPractice →Compute a·u + b·v for 2D vectors.
- A.4 Cross ProductsPractice →Compute the cross product of two 3D vectors.
- A.5 Scalar ProjectionsPractice →Compute the scalar projection of u onto v.
- A.6 Angle Type from the Dot ProductPractice →Classify the angle between vectors as acute, right, or obtuse.
- A.7 Linear Independence (2D)Practice →Decide if columns of a 2×2 matrix are independent.
B.Matrix algebra6 skills
- B.1 2×2 Matrix MultiplicationPractice →Multiply two 2×2 matrices.
- B.2 Matrix-Vector ProductsPractice →Multiply a 2×2 matrix by a 2D vector.
- B.3 2×2 DeterminantsPractice →Compute determinants of 2×2 matrices.
- B.4 3×3 DeterminantsPractice →Expand a 3×3 determinant along the first row.
- B.5 Trace of 2×2Practice →Compute the trace of a 2×2 matrix.
- B.6 2×2 Inverse (Entries)Practice →Find the inverse of an invertible 2×2 matrix (enter det first check).