Free online courseMath Fundamentals Algebra

Conteúdo do Curso

• Video class: Presentation | 1/14 | UPV

  0h03m

• Exercise: In the context of the course on Linear Algebra, how can matrices be applied to solve systems of linear equations?

• Video class: Algebraic equations with one unknown. Ruffini's rule | 2/14 | UPV

  0h13m

• Exercise: What can be concluded if the discriminant (b^2 - 4ac) of a quadratic equation is negative?

• Video class: Linear equations 2 | 3/14 | UPV

  0h10m

• Exercise: What kind of transformations can be used to obtain equivalent linear equations?

• Video class: System of linear equations 2 | 4/14 | UPV

  0h09m

• Exercise: Given a system of linear equations: 3x + 4y = 10 and 6x + 8y = 20, determine the type of system in terms of solutions.

• Video class: Gauss method | 5/14 | UPV

  0h12m

• Exercise: Which of the following best describes a consistent determined system when using the Gauss method to solve linear equations?

• Video class: Examples of systems of linear equations with parameters using the Gauss method | 6/14 | UPV

  0h09m

• Exercise: Which of the following describes a consistent indeterminate system when using the Gauss method to solve a linear equation system with parameters?

• Video class: Definition of Matrix | 7/14 | UPV

  0h07m

• Exercise: Consider a 3x3 matrix with elements a_ij. If the matrix is symmetric, which condition must it satisfy?

• Video class: Operations with matrices | 8/14 | UPV

  0h08m

• Exercise: Which of the following statements about matrix operations is incorrect?

• Video class: Regular matrices | 9/14 | UPV

  0h11m

• Exercise: Which of the following statements is true regarding regular or invertible matrices?

• Video class: Matrix equations | 10/14 | UPV

  0h07m

• Exercise: Given the matrix equation ‘B * X = D’ where B is a 3x3 matrix and D is a 3x3 matrix, what is the size of the matrix X that ensures successful computation of this matrix equation?

• Video class: Determinants | 11/14 | UPV

  0h13m

• Exercise: If a 2x2 square matrix is given as \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), how is its determinant calculated?

• Video class: Matrix Range | 12/14 | UPV

  0h05m

• Exercise: Given a matrix C with dimensions 4x5, what is the maximum possible rank of this matrix?

• Video class: Inverse matrix calculation | 13/14 | UPV

  0h06m

• Exercise: What is the adjoint of the element a_23 in a 3x3 matrix if the complementary submatrix determinant is -5?

• Video class: Cramer's rule | 14/14 | UPV

  0h10m

• Exercise: Consider a 3x3 linear system of equations which can be written in matrix form as A * X = B, where A is the coefficient matrix, X is the vector of unknowns (x, y, z), and B is the vector of independent terms. If the determinant of A is not zero, what does this imply about matrix A?