\( \newcommand{\sech}{\operatorname{sech}} \) \( \newcommand{\inverse}[1]{#1^\leftarrow} \) \( \newcommand{\<}{\langle} \) \( \newcommand{\>}{\rangle} \) \( \newcommand{\vect}{\mathbf} \) \( \newcommand{\veci}{\mathbf{\hat ı}} \) \( \newcommand{\vecj}{\mathbf{\hat ȷ}} \) \( \newcommand{\veck}{\mathbf{\hat k}} \) \( \newcommand{\curl}{\operatorname{curl}\,} \) \( \newcommand{\dv}{\operatorname{div}\,} \) \( \newcommand{\detThree}[9]{ \operatorname{det}\left( \begin{array}{c c c} #1 & #2 & #3 \\ #4 & #5 & #6 \\ #7 & #8 & #9 \end{array} \right) } \) \( \newcommand{\detTwo}[4]{ \operatorname{det}\left( \begin{array}{c c} #1 & #2 \\ #3 & #4 \end{array} \right) } \)

MA 237 Standards

Linear Algebra - 2018 Spring
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  6. MA 237 Standards

At the end of the course, each student should be able to…

  • Module E: Systems of Linear Equations
    • E1: translate back and forth between a system of linear equations and the corresponding augmented matrix.
    • E2: put a matrix in reduced row echelon form.
    • E3: compute the solution set for a system of linear equations.
  • Module V: Vector Spaces
    • V1: explain why a given set with defined addition and scalar multiplication does satisfy a given vector space property, but nonetheless isn’t a vector space.
    • V2: determine if a Euclidean vector can be written as a linear combination of a given set of Euclidean vectors.
    • V3: determine if a set of Euclidean vectors spans \(\mathbb{R}^n\).
    • V4: determine if a subset of \(\mathbb{R}^n\) is a subspace or not.
    • V5: determine if a set of Euclidean vectors is linearly dependent or independent.
    • V6: determine if a set of Euclidean vectors is a basis of \(\mathbb{R}^n\).
    • V7: compute a basis for the subspace spanned by a given set of Euclidean vectors.
    • V8: compute the dimension of a subspace of \(\mathbb{R}^n\).
    • V9: compute a basis for the subspace spanned by a given set of polynomials or matrices.
    • V10: find a basis for the solution set of a homogeneous system of equations.
  • Module A: Algebraic Properties of Linear Maps
    • A1: determine if a map between vector spaces of polynomials is linear or not.
    • A2: translate back and forth between a linear transformation of Euclidean spaces and its standard matrix, and perform related computations.
    • A3: compute a basis for the kernel and a basis for the image of a Euclidean linear map.
    • A4: determine if a given Euclidean linear map is injective and/or surjective.
  • Module M: Matrices
    • M1: multiply matrices.
    • M2: describe the row reduction of a matrix as matrix multiplication.
    • M3: determine if a square matrix is invertible or not.
    • M4: compute the inverse matrix of an invertible matrix.
  • Module G: Geometric Properties of Linear Maps
    • G1: describe how a row operation affects the determinant of a matrix.
    • G2: compute the determinant of a \(4\times 4\) matrix.
    • G3: find the eigenvalues of a \(2\times 2\) matrix.
    • G4: find a basis for the eigenspace of a \(4\times 4\) matrix associated with a given eigenvalue.

Additional topics extending the Theory and Applications of linear algebra are covered by the TA standard.