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- https://math.libretexts.org/Bookshelves/Applied_Mathematics/Contemporary_Mathematics_(OpenStax)/05%3A__Algebra/5.01%3A__Algebraic_ExpressionsThis page focuses on algebraic expressions and equations, detailing how to translate between written and symbolic forms, and explaining operations such as addition, subtraction, multiplication, and di...This page focuses on algebraic expressions and equations, detailing how to translate between written and symbolic forms, and explaining operations such as addition, subtraction, multiplication, and division. It provides examples of expressions versus equations, demonstrates the importance of the order of operations (PEMDAS), and introduces historical context about the symbols used in algebra. Exercises are given for practice, both in translating expressions and performing algebraic operations.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.06%3A_Application_to_Polynomial_InterpolationGiven \(n\) points in \(\mathbb{R}^2\), we solve a linear system to find an appropriate degree polynomial that passes through them.
- https://math.libretexts.org/Courses/Coastline_College/Math_C097%3A_Support_for_Precalculus_Corequisite%3A_MATH_C170/1.02%3A_Algebra_Support/1.2.01%3A_Real_Numbers_Linear_Inequalities_and_Interval_NotationThe vertical line | inside the braces reads, “such that” and the symbol \(\in\) indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all number...The vertical line | inside the braces reads, “such that” and the symbol \(\in\) indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all numbers \(\frac{a}{b}\) such that a and b are elements of the set of integers and b is not equal to zero.” Decimals that terminate or repeat are rational.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.01%3A_Systems_of_Linear_Equations/1.1E%3A_Exercises_for_Section_1.1This page offers exercises on solving linear systems graphically, focusing on finding intersection points of lines, understanding different solution scenarios (no, unique, infinite solutions), and exa...This page offers exercises on solving linear systems graphically, focusing on finding intersection points of lines, understanding different solution scenarios (no, unique, infinite solutions), and examining common intersections of multiple lines or planes. It includes a word problem involving weights of four individuals and tasks requiring the construction of linear systems with defined solution properties and graphical relationships.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/02%3A_Algebra_Support/2.01%3A_Real_Numbers_Linear_Inequalities_and_Interval_NotationThe vertical line | inside the braces reads, “such that” and the symbol \(\in\) indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all number...The vertical line | inside the braces reads, “such that” and the symbol \(\in\) indicates set membership and reads, “is an element of.” The notation above in its entirety reads, “the set of all numbers \(\frac{a}{b}\) such that a and b are elements of the set of integers and b is not equal to zero.” Decimals that terminate or repeat are rational.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.08%3A_SubstitutionThis page covers methods for simplifying non-separable differential equations through substitution, particularly Bernoulli equations, highlighting the significance of making effective substitutions to...This page covers methods for simplifying non-separable differential equations through substitution, particularly Bernoulli equations, highlighting the significance of making effective substitutions to achieve linear forms for easier solutions. It provides examples demonstrating the use of the substitution \(v = \frac{y}{x}\) for homogeneous equations, illustrating the process of transforming complex equations into simpler, separable ones.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.10%3A_Quadratic_Forms/6.10E%3A_Exercises_for_Section_6.10This page discusses quadratic forms in three variables, showing their representation through symmetric matrices. It includes exercises on expressing quadratic expressions in matrix form and transformi...This page discusses quadratic forms in three variables, showing their representation through symmetric matrices. It includes exercises on expressing quadratic expressions in matrix form and transforming them to remove cross-product terms. The content highlights the role of orthogonal matrices in diagonalizing quadratic forms and emphasizes their eigenvalues, focusing on the representation and manipulation of quadratic forms in linear algebra.
