UNC MATH 347: Linear Algebra for Applications
MATH 347 (formerly MATH 547) is UNC's applied linear algebra: matrix algebra, Gaussian elimination, vector spaces, orthogonality and Gram-Schmidt, determinants, and eigenvalues. It's the linear algebra course most majors recommend, serving math, CS, STOR, and quantitative science students.
Fennie is independent and not affiliated with UNC Chapel Hill. This is an unofficial study guide.
What makes it hard
The course pivots mid-stream from comfortable computation (row reduction, matrix arithmetic) to abstraction: subspaces, independence, basis, and dimension demand definition-based reasoning that calculus never required. Students expecting pure matrix mechanics hit the conceptual wall around the vector space unit, and eigenvalue applications at the end assume everything before them fluently.
What you'll cover
- • Matrix algebra and Gaussian elimination
- • Vector spaces and subspaces
- • Linear independence, basis, and dimension
- • Orthogonality and Gram-Schmidt
- • Determinants
- • Eigenvalues and eigenvectors
The MATH 347 study guide
How to study for UNC MATH 347, step by step.
- 1
Memorize the definitions precisely, immediately
Span, independence, basis, subspace, rank: exam reasoning is built from definitions verbatim. Know each one cold, with an example and a non-example attached.
- 2
Make row reduction free early
Gaussian elimination underlies half the course's computations and should cost no thought by week three. Drill it so your attention is available for the abstraction, which is what's actually graded.
- 3
Tie every concept back to Ax = b
Rank, null space, independence, and invertibility are all statements about solutions of linear systems. Keeping that thread visible turns the theorem list into one coherent story, which is the form exams test it in.
- 4
Practice the standard verification arguments
Show a set is a subspace, prove vectors independent, check a map is linear. These short arguments follow patterns, and fluency comes from doing dozens cold, not reading them.
- 5
Give eigenvalues integrated review
The eigen-unit assumes determinants, solving systems, and independence simultaneously. Review those as it approaches, and practice full diagonalization problems end to end.
Today
Today's MATH 347 plan
What a Fennie Daily Plan looks like for MATH 347. Yours is built from your own syllabus and adapts every day to your deadlines and progress.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
FAQ
Is MATH 347 at UNC hard?
Harder than its 'for Applications' name suggests, because the middle of the course is genuinely abstract: subspaces, independence, and basis arguments rather than matrix arithmetic. Students who learn the definitions cold and practice the standard verification arguments do well.
What's the difference between MATH 347 and MATH 577?
MATH 347 is the applied course recommended for most students: tools and usage with lighter theory. MATH 577 (Linear Algebra) is the proof-heavy version for math majors wanting rigor. Check which your program expects; for CS, STOR, and applied tracks, 347 is the standard answer.
What do I need before MATH 347?
Calculus prerequisites per the catalog (MATH 232 or equivalent paths), but the real preparation is tolerance for definition-based reasoning, closer to discrete math than to calculus. If you've seen proofs before, the vector space unit lands much softer.
More UNC courses
MATH 231: Calculus of Functions of One Variable I
MATH 231 is UNC's Calculus I: limits, derivatives, applications of differentiation, and the beginnings of integration. It's required across STEM, pre-health, economics, and CS tracks, and one of the largest math enrollments on campus.
MATH 232: Calculus of Functions of One Variable II
MATH 232 continues UNC's calculus sequence with techniques of integration, applications of the integral, and sequences and series. Campus consensus calls it the harder half of the pair, and it's the prerequisite gateway to MATH 233, STOR 435, and the quantitative tracks.
MATH 233: Calculus of Functions of Several Variables
MATH 233 is UNC's multivariable calculus: vectors, partial derivatives, multiple integrals, and vector calculus through Green's and Stokes' theorems. It's required for math, physics, and quantitative tracks, and a co-requisite companion to PHYS 119.