LACS.PAR.4

LACS.PAR.4

LACS.PAR.4.1Represent a linear system of three equations in three variables as an augmented matrix and reduce the matrix to row-echelon form.LACS.PAR.4.10Solve a matrix equation using inverses; find all solutions to a matrix equation given one solution and the kernel.LACS.PAR.4.11Improve the simple authentication scheme over GF(2).LACS.PAR.4.12Show and explain how threshold secret sharing works in conjunction with Gaussian elimination through programming.LACS.PAR.4.13Write code utilizing error-correcting concepts.LACS.PAR.4.2Interpret 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.4.3Determine 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.4.4Interpret linear dependence of vectors geometrically.LACS.PAR.4.5Find 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.LACS.PAR.4.6Add two matrices, multiply a matrix by a scalar, find the transpose of a matrix.LACS.PAR.4.7Determine 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.4.8Determine 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.4.9Decompose a matrix into its symmetric and skew-symmetric parts; decompose a matrix into its LU factorization.
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