LACS.PAR.8: LACS.PAR.8

LACS.PAR.8

LACS.PAR.8.1Evaluate the determinant of a matrix along any row or column and use a recursive procedure for evaluating a determinant for matrices larger than 3-by-3.LACS.PAR.8.10Find the dimension of the eigenspace corresponding to the eigenvalues of a symmetric matrix.LACS.PAR.8.11Determine an orthogonal matrix that diagonalizes a given matrix.LACS.PAR.8.12Apply eigenvalues and eigenvectors to problems in context.LACS.PAR.8.2Justify properties of the determinant.LACS.PAR.8.3Calculate the determinant of the product of two matrices; calculate the determinant of the transpose of a matrix.LACS.PAR.8.4Determine if a matrix has a nonzero determinant and extend the nonzero determinant property to problems involving linear dependency, rank, and matrix inverses.LACS.PAR.8.5Extend the definition and geometric interpretation of the cross product to n – 1 vectors in n dimensions.LACS.PAR.8.6Use Cramer’s Rule to solve a system of linear equations.LACS.PAR.8.7Find the characteristic polynomial of a matrix and interpret the characteristic polynomial geometrically.LACS.PAR.8.8Find the eigenvalues and eigenvectors of a matrix and interpret them geometrically.LACS.PAR.8.9Use a basis of eigenvectors to create a change of basis matrix.
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