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Systems of Linear Equations
Linear Equations continued
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affine transformation arbitrary axioms basis vectors chain rule coefficients column vectors components compute Consider continuously differentiable coordinate functions coordinate system curvilinear coordinate defined parametrically denned determinant function differentiable at Xo differentiable function dimension domain space dx dy dxof elementary equation euclidean space Example Exercise exists Find formula function Rn geometric given graph Hence implicitly defined inequality inner product intersection inverse function theorem iterated integral Jacobian matrix kernel length linear combination linear transformation linearly independent n-dimensional nonzero norm numerical multiplication one-one orthonormal basis parallelogram parallelotope partial derivatives perpendicular point Xo properties Prove quadratic polynomial range real numbers real-valued function rectangle region Riemann Riemann integral satisfies Section Show shown in Figure solution subset subspace Suppose surface tangent plane Taylor expansion variable vector function vector space 9C vectors Xi volume zero