Linear Algebra MATH 203
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This 1 page Class Notes was uploaded by Michale Kuhlman on Monday September 28, 2015. The Class Notes belongs to MATH 203 at George Mason University taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/215010/math-203-george-mason-university in Mathematics (M) at George Mason University.
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Date Created: 09/28/15
REVIEW SHEET FOR EXAM 1 SPRING 2008 MATH 203 The exam will cover the material we have discussed in class and studied in homework7 from Section 11 to Section 110 The following list points out the most important de nitions and theorems I De nitions D t o The de nition of Ax in both words and symbols 0 SpanV7 Spanu7 V and geometric interpretation in R 2 or R 3 o SpanV1Vp o Linearly independent and linearly dependent 0 Linear transformation 0 Standard matrix of a linear transformation Theorems in Chapter 1 0 Theorem 2 Existence and Uniqueness Theorem 0 Theorem 3 Matrix equation7 vector equation7 system of linear equations 0 Theorem 4 When do the columns of A span R In7 0 Theorem 5 Properties of the Matrix Vector Product Ax 0 Theorem 6 Solution format of Matrix Equations 0 Theorems 77 87 9 Properties of linearly dependent sets III Important Skills partial list 0 Use the Gauss Elimination Process to solve linear systems 0 Determine when a system is consistent Write the general solution in parametric vector form 0 Determine values of parameters that make a system consistent7 or make the solution unique 0 Determine when a homogeneous system has a nontrivial solution 0 Determine when a vector is in a subset spanned by speci ed vectors 7 Exhibit a vector as a linear combination of speci ed vectors 7 Determine whether a speci ed vector is in the range of a linear transformation
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