TBIL Activities for Understanding Linear Algebra

Objectives

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  I can determine if a matrix is invertible, and if so, compute its inverse.
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  I can invert an appropriate matrix to solve a system of linear equations.
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  I can explain why a set of Euclidean vectors is or is not a basis of ${\mathbb{R}}^n\text{.}$
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  I can compute a basis for the subspace spanned by a given set of Euclidean vectors, and determine the dimension of the subspace.
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  I can find a basis for the solution set of a homogeneous system of equations.
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  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.
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  I can describe how a row operation affects the determinant of a matrix.
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  I can compute the determinant of a $4\times 4$ matrix.
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  I can determine if a subset of ${\mathbb{R}}^n$ is a subspace or not.