Skip to main content ☰ Contents Index You! < Prev ^ Up Next > \(\newcommand{\avec}{{\mathbf a}}
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Chapter 3 TBIL Activities: Invertibility, Bases, and Coordinate Systems
Objectives
I can determine if a matrix is invertible, and if so, compute its inverse.
I can invert an appropriate matrix to solve a system of linear equations.
I can explain why a set of Euclidean vectors is or is not a basis of \(\IR^n\text{.}\)
I can compute a basis for the subspace spanned by a given set of Euclidean vectors, and determine the dimension of the subspace.
I can find a basis for the solution set of a homogeneous system of equations.
I can compute a basis for the null space and a basis for the column space of a linear map, and verify that the rank-nullity theorem holds for a given linear map.
I can describe how a row operation affects the determinant of a matrix.
I can compute the determinant of a \(4\times 4\) matrix.
I can determine if a subset of \(\IR^n\) is a subspace or not.
