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CHAPTER 1MATRICES AND VECTORS
CHAPTER 3LINEAR SPACES
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applying elementary row arbitrary array of numbers arrows basic probability vector Cartesian coordinate system Chapter Check coefficient column vector Compute concepts consists defined denoted Determine diagonal dimension dot-product elementary row operations elements equation AX example Exercise Find a parametric following systems formula geometric Hence hyperplane identity matrix interpreted intersection inverse leading term leading unknowns linear algebra linear combination linear equations linear space linear subspace linear transformation linearly independent system minimal distance n x n)-matrix n-column n-tuples nonzero rows number of solutions number of vectors obtained parallel parameters parametric expression perpendicular Problem Prove random variable rank reduce reduction to row-echelon row-echelon form row-echelon matrix scalar multiples sets of vectors shift Show solution set solution-set solutions of AX solving square matrix standard deviation subset superfluous surjective system of vectors system Sf systems of linear Theorem tion unique solution units in direction vector-space Xu X2 zero