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Click the View full text link to bypass dynamically loaded article content. This chapter moves on to higher-dimensional linear algebra. The concepts of linear independence, subspace, and spanning set arise. Important topics include invertible matrices and reduced row echelon form of matrices. It is shown that a linear system of algebraic equations has a unique solution if and only if the corresponding matrix is invertible. The special cases of real eigenvalues, complex eigenvalues, and repeated eigenvalues are treated in detail.