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Georgia standard · Mathematics

LACS.PAR.7Vector Space Applications

Solve contextual, mathematical problems using vector spaces to explain real-life phenomena.

Appears in: Mathematics, High School

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Expectations

  • Use properties of vector spaces to solve problems.

    • LACS.PAR.7.1

      Determine whether a given set of vectors generates a vector space.

    • LACS.PAR.7.2

      Justify whether a subset of a vector space is a subspace.

    • LACS.PAR.7.3

      Determine whether a given vector is in the linear span of a set of vectors.

    • LACS.PAR.7.4

      Determine whether two vector subspaces are orthogonal; find the orthogonal component of a given subspace.

  • Find and use vectors as a basis.

    • LACS.PAR.7.5

      Determine whether a set of vectors is a basis for a vector space.

    • LACS.PAR.7.6

      Find the dimension of a vector space; find the dimensions of the row space, column space, and kernel for a given matrix; find the rank of a matrix.

    • LACS.PAR.7.7

      Find a matrix representing a linear map.

    • LACS.PAR.7.8

      Determine the change of representation for a linear transformation given two different bases on a vector space.

    • LACS.PAR.7.9

      Determine if two matrices are similar; determine if two matrices are orthogonal.

    • LACS.PAR.7.10

      Find an orthogonal basis for a given basis or subspace by applying the Gram-Schmidt orthonormalization process.

    • LACS.PAR.7.11

      Perform QR factorization of a matrix to solve matrix equations.

  • Apply vector spaces and vectors as a basis in programming to solve contextual problems.

    • LACS.PAR.7.12

      Apply the method of least squares to find the line or parabola of best fit to approximate data in context.

    • LACS.PAR.7.13

      Apply the grow-and-shrink algorithm in the minimum spanning forest problem in GF(2).

    • LACS.PAR.7.14

      Apply the Exchange Lemma to image perspective rendering.

    • LACS.PAR.7.15

      Use bases to represent images and sounds as wavelets; perform wavelet transformation, implementation, and decomposition through programming.

    • LACS.PAR.7.16

      Program a Fast Fourier Transform to store a sequence of amplitude samples.

    • LACS.PAR.7.17

      Apply the Rank Theorem to demonstrate the simple authentication scheme.

Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.

LACS.PAR.7: Vector Space Applications | Georgia Mathematics Standard | Georgia Homeroom