Elementary Linear AlgebraThis classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.Clear, accessible, step-by-step explanations make the material crystal clear.The authors spotlight the relationships between concepts to give a unified and complete picture.Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues. |
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3-space a₁x angle approximation augmented matrix axioms b₁ b₂ c₁ C₂ called cofactor expansion column vectors components computations conic coordinate matrix coordinate vector defined denoted det(A determine diagonalizable dimensional vector space dominant eigenvalue dominant eigenvector E₁ eigenspace corresponding eigenvalues eigenvector elementary matrix elementary product entries Euclidean inner product EXERCISE SET Figure finite dimensional vector formula Gaussian elimination initial point inner product space integer invertible matrix k₁ k₂ linear combination linear equations linear transformation linearly independent linearly independent set nonzero vectors obtain orthonormal basis orthonormal set P₁ P₂ permutation plane polynomials proof Prove real numbers reduced row-echelon form result row space row-echelon form scalar multiplication second row set of vectors Show spanned square matrix standard position subspace system of equations system of linear T(v₁ third row transition matrix u₁ u₂ v₁ v₂ vector space w₁ w₂ x'y'-coordinate x₁ yields zero