Math
Linear Algebra I
Train on Linear Algebra I with 300 published problems. Preview a problem, explore the course outline, and work through one problem at a time.
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Preview a course problem
See a problem from Linear Algebra I before you begin.
Course topics
Course topics
Vector spaces, subspaces, sums, and direct sums
Linear independence, bases, and dimension
Linear maps, kernels, images, and rank-nullity
Quotient spaces and universal factorization
Dual spaces, annihilators, and transpose maps
Alternating forms and determinant structure
Practice problems
Try a few Linear Algebra I problems, each with a hint.
- The union of two axes is not a subspace Free with an accountVector spaces, subspaces, sums, and direct sums
- The sum map detects an internal direct sum Free with an accountVector spaces, subspaces, sums, and direct sums
- Restrict an independent family Linear independence, bases, and dimension
- Complete an independent family Linear independence, bases, and dimension
- A composite preserves two-term linear combinations Linear maps, kernels, images, and rank-nullity
- Equal dimensions tie injectivity to surjectivity Linear maps, kernels, images, and rank-nullity
- Evaluating a map induced on a quotient Quotient spaces and universal factorization
- Constructing the second-isomorphism map Quotient spaces and universal factorization
- Annihilator of an arbitrary generated supremum Dual spaces, annihilators, and transpose maps
- Transpose does not change determinant Alternating forms and determinant structure