Linear Algebra I

Vectors, matrices and systems of linear equations, the language of engineering computation.

MATH-125 Year 1 3 credits 12 lessons · 6 h 55 min

Offered by HSM University · Engineering Core

What you'll learn

Work with vectors: magnitude, dot product, cross product, angles, lines and planes
Form linear combinations, determine spans, test linear independence and find coordinates in a basis
Solve systems of linear equations by Gaussian elimination and interpret their solution sets
Multiply, transpose and invert matrices and use them to model engineering systems
Solve systems with LU and Cholesky factorizations, estimate computational cost, and assess conditioning
Compute determinants and interpret them as area and volume scale factors and tests of invertibility
Find column spaces, null spaces and rank, and apply the rank-nullity theorem to trusses and circuits
Represent rotations, scalings, shears, projections and translations as matrices and compose them
Find eigenvalues and eigenvectors, diagonalize matrices and compute matrix powers
Use orthogonal projections, Gram-Schmidt and the normal equations to fit models by least squares
Apply the spectral theorem to principal stresses, vibration modes and data, and interpret the SVD
Formulate engineering problems in matrix form, solve them with appropriate methods and interpret the results

12 lessons · 6 h 55 min total · final exam

Vectors, matrices and systems of linear equations, the language of engineering computation.

Part of the Engineering stream, typically taken in year 1.