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About 9 results
  • https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/06%3A_Systems_of_ODEs/6.04%3A_Matrices_and_linear_systems/6.4E%3A_Exercises_for_Section_6.4
    This page features an exercise set focused on matrix operations, including solving systems of equations with matrix inverses, computing determinants, and exploring matrix invertibility conditions. It ...This page features an exercise set focused on matrix operations, including solving systems of equations with matrix inverses, computing determinants, and exploring matrix invertibility conditions. It includes tasks like determining invertibility for matrices with variables, verifying matrix relationships, and provides solutions for all exercises. Key examples focus on determinant calculation and identifying nonzero matrices that meet specific multiplication criteria.
  • https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/07%3A_Vector_Spaces/7.04%3A_Linear_Independence/7.4E%3A_Exercises_for_Section_7.4
    This page discusses exercises on linear independence of vectors and polynomials. It concludes that a specific set of polynomials is linearly independent, while another set is determined to be linearly...This page discusses exercises on linear independence of vectors and polynomials. It concludes that a specific set of polynomials is linearly independent, while another set is determined to be linearly dependent with a provided linear combination. Additional exercises examine conditions for independence in polynomial collections and propose proof methods for assessing the independence of three polynomials in a given space.
  • https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/04%3A_Power_series_methods/4.03%3A_Singular_Points_and_the_Method_of_Frobenius
    While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be luc...While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.
  • https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.11%3A_Least_Squares_Approximation/4.11.E%3A_Exercises_for_Section_4.11
    This page provides exercises on finding least squares solutions for systems of equations and determining best fit lines for data points. It includes practical problems for deriving solutions and formu...This page provides exercises on finding least squares solutions for systems of equations and determining best fit lines for data points. It includes practical problems for deriving solutions and formulas for closest points to planes with scalar equations, applying concepts from linear regression and optimization in both two-dimensional and three-dimensional contexts.
  • https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/05%3A_The_Laplace_Transform/5.03%3A_Convolution/5.3E%3A_Exercises_for_Section_5.3
    This page covers exercises on convolution computations relevant to differential equations and integral solutions. It includes tasks like finding convolutions, solving linear differential equations wit...This page covers exercises on convolution computations relevant to differential equations and integral solutions. It includes tasks like finding convolutions, solving linear differential equations with initial conditions, and using convolution to derive answers with specific functions. The findings are presented through integrals or function forms, emphasizing the application of convolution in addressing differential equations and Laplace transforms.
  • 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_Interpolation/1.6E%3A_Exercises_for_Section_1.7
    This page discusses exercises on interpolating polynomials from specified data points, detailing degrees for each polynomial. Solutions include a degree 2 polynomial for initial data sets and a degree...This page discusses exercises on interpolating polynomials from specified data points, detailing degrees for each polynomial. Solutions include a degree 2 polynomial for initial data sets and a degree 3 polynomial for another. Explanations address issues such as collinear points, distinct points with zero y-components, and overlapping x-components, which complicate polynomial determination.
  • 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_1.1
    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 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/Bookshelves/Applied_Mathematics/Introduction_to_Game_Theory%3A_A_Discovery_Approach_(Nordstrom)/01%3A_What_is_Game_Theory/1.01%3A_Players_and_Strategies
    In this book, most of the games will be played by two players. Each player must decide how he or she will play the game. In order to study games mathematically, we need to make some assumptions about ...In this book, most of the games will be played by two players. Each player must decide how he or she will play the game. In order to study games mathematically, we need to make some assumptions about how the players should play the game. This allows us to be able to better predict what our players should do. The example given in this section illustrates the characteristics we will assume about our players.
  • https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/02%3A_Matrices/2.03%3A_Elementary_Matrices/2.3E%3A_Exercises_for_Section_2.3
    This page includes exercises that help identify elementary matrices linked to specific row operations on matrices. The exercises involve deriving an elementary matrix E that transforms a matrix \(...This page includes exercises that help identify elementary matrices linked to specific row operations on matrices. The exercises involve deriving an elementary matrix E that transforms a matrix A into another matrix B, finding the inverse of these matrices, and proving properties like invertibility and the nature of their products.

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