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INTRODUCTION TO VECTORS
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augmented matrix basic solution called cancellation law Chapter coefficient matrix cofactor commutative complete solution complex numbers consistent system convex set Cramer's rule defined Definition determinant distributive law echelon matrix echelon method elementary matrix elementary operation elementary row operations equivalence relation Example EXERCISES exist expressed extreme point Factory following theorem geometric given graph Hermitian identity element inequality infinite number integers integral domain interchange inverse linear combination linear equations linear programming linearly independent main diagonal mathematical system matrices with scalar matrix addition matrix multiplication maximum minimum problem nonsingular nonzero notation number of solutions postulates proof of Theorem Prove Theorem rank real numbers ring row equivalent scalar entries scalar matrix scalar product Section simplex method skew-symmetric skew-symmetric matrix solve square matrix student submatrix symmetric matrix system of equations system of linear Theorem 9 transformation transpose unique solution units unknowns vector space Verify zero