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Chapter 1 Systems of Linear Equations
Chapter 2 Matrix Algebra
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augmented matrix basis vectors calculate characteristic equation characteristic polynomial coefﬁcient column space column vector complex conjugate complex numbers complex vector space components Consider Cramer’s rule deﬁned Demystiﬁed det|A diagonal elements eigenvalues eigenvectors elementary matrix elementary row operations entry EXAMPLE ﬁnd Find the determinant Find the eigenvalues Find the matrix ﬁrst column ﬁrst equation ﬁrst pivot ﬁrst row Gauss-Jordan elimination given gives Hermitian conjugate Hermitian matrix identity matrix inverse linear combination linear equations linear system linear transformation linearly independent lower triangular matrix matrix multiplication matrix representation McGraw-Hill Companies normalized eigenvectors null space number of rows obtain orthogonal orthonormal basis real numbers reduce the matrix row and column row canonical form row echelon form row space row vector satisﬁed scalar multiplication second row Show span standard basis subspace symmetric matrices Systems of Linear Take the transpose unitary matrix vector addition write zero vector