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Systems of Linear Equations
Finding the Inverse of a Matrix
12 other sections not shown
according to Theorem addition and scalar approximation associated basis for R2 basis matrix calculus called change of basis coefficients collinear column space Compute coordinate matrix deﬁned deﬁnition determinant dot product eigenfunction eigenspace eigenvalue eigenvectors elementary matrix equal Exercises ﬁrst form a basis function f Gaussian elimination given gives Gram-Schmidt process graph Hence Hint homogeneous system Ax identity matrix inner product space integer invertible matrix isomorphism iteration linear combination linear operator linear span linear transformation linearly independent m x n matrix transformation method n x n matrix node nonzero vector obtained one-to-one ordered basis orthonormal basis pictured in Figure plane polynomials proof Prove real numbers reduced row echelon rotation row echelon form row operations scalar multiplication scale factor Section sequence set of vectors solution set solution space solve square matrix Step subspace Suppose system of equations vector space vectors in R2 vectors v1 x-direction zero vector