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Test: Introduction to linear algebra

Gap-fill exercise

Write the correct answers. Every gap must be filled by one only word. When finished press Check. Pressing the Hint button adds the next correct letter in the answer.

An equation like ax = b is called a equation. It is a degree equation in one . The solution of this equation may be interpreted in a cartesian coordinate system as the point of two lines. The solution of this equation is a in the real line, while the solutions of a linear equation in two unknowns can be represented as a in the plane and those of a linear equation in three unknowns as a in tridimensional space. A linear equation in two unknowns has always many solutions. A system of two linear equations in two unknowns may have solutions, only solution or many solutions. The system has no solutions if the two equations represent lines.
A matrix is a rectangular of real numbers. Matrix multiplication is associative, but not always .
Given a linear system of m equations in n unknowns, the matrix whose entries are all the coefficients and constants of the system is called the matrix of the system. If a matrix is in row-echelon form the leftmost non zero entry of a row is called a , and the number of these leading elements of the rows is called the of the system. The algorithm used to reduce matrices in row-echelon form is called the - algorithm. A system that has no solutions is called .