The Linear Algebra course was developed through the Ohio Department of Higher ...

The Linear Algebra course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in November 2018. The course is part of the Ohio Transfer Module and is also named OMT019. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadAnna Davis Ohio Dominican UniversityContent ContributorsPaul Bender Ohio Dominican UniversityRosemarie Emanuele Ursuline CollegePaul Zachlin Lakeland Community CollegeLibrarianDaniel Dotson Ohio State University Review TeamJim Fowler Ohio State UniversityJim Cottrill Ohio Dominican University

We establish that a plane is determined by a point and a ...

We establish that a plane is determined by a point and a normal vector, and use this information to derive a general equation for planes in R^3.https://ximera.osu.edu/la/LinearAlgebra/RRN-M-0030/main

We introduce standard unit vectors in R^2, R^3 and R^n, and express a given vector as ...

We introduce standard unit vectors in R^2, R^3 and R^n, and express a given vector as a linear combination of standard unit vectors.https://ximera.osu.edu/la/LinearAlgebra/VEC-M-0035/main

We state and prove the cosine formula for the dot product of ...

We state and prove the cosine formula for the dot product of two vectors, and show that two vectors are orthogonal if and only if their dot product is zero.https://ximera.osu.edu/la/LinearAlgebra/VEC-M-0060/main

We find the projection of a vector onto a given non-zero vector, ...

We find the projection of a vector onto a given non-zero vector, and find the distance between a point and a line.https://ximera.osu.edu/la/LinearAlgebra/VEC-M-0070/main

We define the determinant of a square matrix in terms of cofactor ...

We define the determinant of a square matrix in terms of cofactor expansion along the first row.https://ximera.osu.edu/la/LinearAlgebra/DET-M-0010/main

We define the determinant of a square matrix in terms of cofactor ...

We define the determinant of a square matrix in terms of cofactor expansion along the first column, and show that this definition is equivalent to the definition in terms of cofactor expansion along the first row.https://ximera.osu.edu/la/LinearAlgebra/DET-M-0020/main

We examine the effect of elementary row operations on the determinant and ...

We examine the effect of elementary row operations on the determinant and use row reduction algorithm to compute the determinant.https://ximera.osu.edu/la/LinearAlgebra/DET-M-0030/main

We explore the theory behind finding the eigenvalues and associated eigenvectors of ...

We explore the theory behind finding the eigenvalues and associated eigenvectors of a square matrix.https://ximera.osu.edu/la/LinearAlgebra/EIG-M-0020/main

In this module we discuss algebraic multiplicity, geometric multiplicity, and their relationship ...

In this module we discuss algebraic multiplicity, geometric multiplicity, and their relationship to diagonalizability.https://ximera.osu.edu/la/LinearAlgebra/EIG-M-0050/main

We define a linear combination of vectors and examine whether a given ...

We define a linear combination of vectors and examine whether a given vector may be expressed as a linear combination of other vectors, both algebraically and geometrically.https://ximera.osu.edu/la/LinearAlgebra/VEC-M-0040/main

We define the span of a collection of vectors and explore the ...

We define the span of a collection of vectors and explore the concept algebraically and geometrically.https://ximera.osu.edu/la/LinearAlgebra/VEC-M-0090/main

We define linear independence of a set of vectors, and explore this ...

We define linear independence of a set of vectors, and explore this concept algebraically and geometrically.https://ximera.osu.edu/la/LinearAlgebra/VEC-M-0100/main

We define a linear transformation from R^n into R^m and determine whether a given transformation is ...

We define a linear transformation from R^n into R^m and determine whether a given transformation is linear.https://ximera.osu.edu/la/LinearAlgebra/LTR-M-0010/main

We establish that every linear transformation of R^n is a matrix transformation, and define ...

We establish that every linear transformation of R^n is a matrix transformation, and define the standard matrix of a linear transformation.https://ximera.osu.edu/la/LinearAlgebra/LTR-M-0020/main

We define linear transformation for abstract vector spaces, and illustrate the definition ...

We define linear transformation for abstract vector spaces, and illustrate the definition with examples.https://ximera.osu.edu/la/LinearAlgebra/LTR-M-0022/main

We establish that a linear transformation of a vector space is completely ...

We establish that a linear transformation of a vector space is completely determined by its action on a basis.https://ximera.osu.edu/la/LinearAlgebra/LTR-M-0025/main

We define composition of linear transformations, inverse of a linear transformation, and ...

We define composition of linear transformations, inverse of a linear transformation, and discuss existence and uniqueness of inverses.https://ximera.osu.edu/la/LinearAlgebra/LTR-M-0030/main

We introduce matrices, define matrix addition and scalar multiplication, and prove properties ...

We introduce matrices, define matrix addition and scalar multiplication, and prove properties of those operations.https://ximera.osu.edu/la/LinearAlgebra/MAT-M-0010/main

We introduce matrix-vector and matrix-matrix multiplication, and interpret matrix-vector multiplication as linear ...

We introduce matrix-vector and matrix-matrix multiplication, and interpret matrix-vector multiplication as linear combination of the columns of the matrix.https://ximera.osu.edu/la/LinearAlgebra/MAT-M-0020/main

We define the transpose of a matrix and state several properties of ...

We define the transpose of a matrix and state several properties of the transpose. We introduce symmetric, skew symmetric and diagonal matrices.https://ximera.osu.edu/la/LinearAlgebra/MAT-M-0025/main

We interpret linear systems as matrix equations and as equations involving linear ...

We interpret linear systems as matrix equations and as equations involving linear combinations of vectors. We define singular and nonsingular matrices.https://ximera.osu.edu/la/LinearAlgebra/MAT-M-0030/main

We solve systems of equations in two and three variables and interpret ...

We solve systems of equations in two and three variables and interpret the results geometrically.https://ximera.osu.edu/la/LinearAlgebra/SYS-M-0010/main

We introduce the augmented matrix notation and solve linear system by carrying ...

We introduce the augmented matrix notation and solve linear system by carrying augmented matrices to row-echelon or reduced row-echelon form.https://ximera.osu.edu/la/LinearAlgebra/SYS-M-0020/main

We introduce Gaussian elimination and Gauss-Jordan elimination algorithms, and define the rank of a ...

We introduce Gaussian elimination and Gauss-Jordan elimination algorithms, and define the rank of a matrix.https://ximera.osu.edu/la/LinearAlgebra/SYS-M-0030/main

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