LACS.PAR.4Matrix Applications in Context

Expectations

• Use matrices to solve systems of linear equations.

  • LACS.PAR.4.1

    Represent a linear system of three equations in three variables as an augmented matrix and reduce the matrix to row-echelon form.

  • LACS.PAR.4.2

    Interpret the nature of the solution of a system from its row-echelon form, and if there are infinitely many solutions, express them as a vector equation.

  • LACS.PAR.4.3

    Determine whether a vector is a linear combination of other given vectors; find the linear combination of vectors that results in a given vector.

  • LACS.PAR.4.4

    Interpret linear dependence of vectors geometrically.

  • LACS.PAR.4.5

    Find the kernel of a matrix and explore the relationship between the kernel, the orthogonality of the vectors in the kernel, and the linear dependence of the rows/columns.

• Operations on and with matrices.

  • LACS.PAR.4.6

    Add two matrices, multiply a matrix by a scalar, find the transpose of a matrix.

  • LACS.PAR.4.7

    Determine when matrix multiplication is defined, and if defined, multiply two matrices by considering the matrix product as a dot product of a group of vectors.

  • LACS.PAR.4.8

    Determine when the inverse of a square matrix exists, and if it exists, find it by augmenting the identity matrix to the matrix and then use row operations.

  • LACS.PAR.4.9

    Decompose a matrix into its symmetric and skew-symmetric parts; decompose a matrix into its LU factorization.

  • LACS.PAR.4.10

    Solve a matrix equation using inverses; find all solutions to a matrix equation given one solution and the kernel.

• Solve applied problems involving matrices using programming.

  • LACS.PAR.4.11

    Improve the simple authentication scheme over GF(2).

  • LACS.PAR.4.12

    Show and explain how threshold secret sharing works in conjunction with Gaussian elimination through programming.

  • LACS.PAR.4.13

    Write code utilizing error-correcting concepts.

Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.