09_23_terms_to_know

09_23_terms_to_know - Ax = b is obtained by translating the...

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Prelim Prep: Concepts (1.3-3.4) MA2940: Linear Algebra for Engineers Terms to be Familiar With: Linear Combination Linearly Independent Vectors Linearly Dependent Vectors Singular Matrix/ Invertible Matrix Upper/Lower Triangular Matrix Back Substitution Pivot/Pivot Multiplier Permutation Matrix Matrix Factorization Elementary Matrix Elimination Augmented Matrix Gauss-Jordan Elimination Symmetric Matrix LU Decomposition/ LDU Decomposition Transpose Inner/Outer Product Vector Space Subspace Column Space Span Nullspace of a Matrix Special Solution Pivot/Free Columns Row Echelon Form Reduced Row Echelon Form Rank of a Matrix Complete Solution Full Column/Row Rank True/False Questions ( T / F ) The equation x = x 2 u + x 3 v , with x 2 and x 3 free (and neither u or v a multiple of the other), describes a plane through the origin. ( T / F ) The solution set of
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Unformatted text preview: Ax = b is obtained by translating the solution set of Ax = 0. • ( T / F ) The columns of the matrix A are linearly independent if the equation Ax = 0 has the trivial solution. • ( T / F ) If S is a linearly dependent set, then each vector is a linear combination of the other vectors in S . • ( T / F ) Let A and B be m × n matrices. If A is row-equivalent to B , then Col ( A ) = Col ( B ). ( Col ( A ) is the column space of A .) • ( T / F ) The vectors running from the origin to the plane defined by the equation x + 2 y + 3 z = 0 form a subspace of R 4 . • ( T / F ) If addition is redefined as a ⊕ b = a + 2 b , then R 2 using this new addition is not a vector space. 1 TA: Kyle Wilson...
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This note was uploaded on 01/02/2012 for the course MATH 2940 at Cornell.

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