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Georgia standard · Mathematics

`LACS.PAR.8`Eigenvalue Real-Life Applications

Solve contextual, mathematical problems using eigenvalues and eigenvectors to explain real-life phenomena.

Appears in: Mathematics, High School

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Expectations

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

Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.