Appendix B Proteus questions
1.2 Finding solutions to linear systems
Checkpoint 1.2.8 Linear systems and augmented matrices
Checkpoint 1.2.9 Identifying reduced row echelon form
Checkpoint 1.2.10 Implementing Gaussian elimination
Checkpoint 1.2.11 Do elementary row operations to achieve RREF
Checkpoint 1.2.12 Determine the number of solutions from RREF
1.4 Pivots and their influence on solution spaces
Checkpoint 1.4.6 Pivots and the solution sets of linear systems
Checkpoint 1.4.7 The shape of a matrix and consistency
Checkpoint 1.4.8 The shape of a matrix and solutions to a linear system
2.2 Matrix multiplication and linear combinations
Checkpoint 2.2.9 Determining if a vector is a linear combination of a set of vectors
Checkpoint 2.2.10 Writing a vector as a linear combination of other vectors in three ways
Checkpoint 2.2.11 Connecting linear combinations and matrix multiplication
Checkpoint 2.2.12 Algebraic properties of matrix multiplication
Checkpoint 2.2.13 Representing linear systems
2.3 The span of a set of vectors
Checkpoint 2.3.16 Describing span geometrically
Checkpoint 2.3.17 Describing span algebraically
Checkpoint 2.3.18 Connecting span with reduced row echelon form
Checkpoint 2.3.19 Identifying vectors in the span of a set of vectors
Checkpoint 2.3.20 Understanding Span - True/False/Sometimes
2.4 Linear independence
Checkpoint 2.4.11 Defining the concept of linear dependence
Checkpoint 2.4.12 A review of linear independence
Checkpoint 2.4.13 Recognizing linear independence
2.6 The geometry of matrix transformations
Checkpoint 2.6.19 Seeing matrix transformations as functions
Checkpoint 2.6.20 Finding matrices of transformations
Checkpoint 2.6.21 Finding matrices of transformations graphically
Checkpoint 2.6.23 Algebraic properties of matrix transformations
Checkpoint 2.6.24 Identifying matrix transformations graphically
3.1 Invertibility
Checkpoint 3.1.11 Determining the invertibility of matrices
Checkpoint 3.1.12 Determining conditions for invertibility
Checkpoint 3.1.13 Connecting invertibility to solutions of equations
3.2 Bases and coordinate systems
Checkpoint 3.2.13 Defining the concept of basis
Checkpoint 3.2.14 Recognizing the properties of a basis
Checkpoint 3.2.15 Explaining change of basis
Checkpoint 3.2.16 Changing coordinate representations algebraically
Checkpoint 3.2.17 Changing coordinate representations graphically
Checkpoint 3.2.19 Changing coordinates between several bases
3.5 Subspaces
Checkpoint 3.5.14 Defining the column space
Checkpoint 3.5.15 Describing properties of subspaces
Checkpoint 3.5.16 Determining elements of spaces
Checkpoint 3.5.17 Determining dimensions of subspaces
4.1 An introduction to eigenvalues and eigenvectors
Checkpoint 4.1.9 Using the definition of eigenvectors and eigenvalues
Checkpoint 4.1.10 Identifying eigenvectors and eigenvalues of a matrix
Checkpoint 4.1.11 Applying linearity to products of eigenvectors
Checkpoint 4.1.12 Using eigenvectors in computations involving matrix powers
4.2 Finding eigenvalues and eigenvectors
Checkpoint 4.2.15 Reasoning about eigenvectors and eigenvalues
Checkpoint 4.2.16 Finding and using eigenvectors
Checkpoint 4.2.17 Reasoning with the characteristic polynomial
Checkpoint 4.2.18 Determining when there is a basis of eigenvectors
Checkpoint 4.2.19 Proving the characteristic polynomial condition
Checkpoint 4.2.20 Finding examples of matrices with multiplicity 2
4.3 Diagonalization, similarity, and powers of a matrix
Checkpoint 4.3.13 Constructing a matrix from its eigenvalues and eigenvectors
Checkpoint 4.3.14 Diagonalizing a matrix
Checkpoint 4.3.15 Reasoning about diagonalizable matrices
Checkpoint 4.3.16 Conditions affecting diagonalizability
Checkpoint 4.3.17 Determining when a matrix is diagonalizable
Checkpoint 4.3.19 Proving similar matrices have the same determinant
6.2 Orthogonal complements and the matrix transpose
Checkpoint 6.2.16 Reasoning about the matrix transpose and orthogonality
Checkpoint 6.2.19 The complement of a plane
Checkpoint 6.2.20 Dimensions of column spaces and null spaces
Checkpoint 6.2.21 Placing vectors in subspaces
6.3 Orthogonal bases and projections
Checkpoint 6.3.24 Determining weights from dot products
Checkpoint 6.3.25 Reasoning about an orthogonal basis
Checkpoint 6.3.26 Determining orthogonality
Checkpoint 6.3.27 Reasoning about orthogonal projections
