Study Guide for Final Exam

# Study Guide for Final Exam - Linear Algebra (1) Know the...

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Linear Algebra (1) Know the properties of: a. Matrix Inverses, Transpose, Determinants, Dot, Cross and Scalar Triple Products, Length of a Vector (2) Know what the trace of a matrix A is, a symmetric matrix is , an orthonormal matrix is , a Quadratic form is (3) Know the types of Systems of Linear Equations, i.e. underdetermined , determined and overdetermined (4) Know Cramer’s Rule, Know how to recognize the Row-Echelon form and Reduced Row-Echelon form, Know what the 3 types of elementary matrices are. (5) Know the definition of:linear independence, a basis, an orthonormal basis, the Range and Nullspace of a matrix A and A T , the Rank and Nullity of a matrix A, the characteristic equation, eigenvalues, eigenvectors. (6) How to find eigenvalues ( including Gerschgorin’s Theorem, Synthetic Division and finding the list of possible rational roots) , How to find the corresponding eigenvectors, How to find Transition Matrices. Do you know how to:

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## Study Guide for Final Exam - Linear Algebra (1) Know the...

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