Podcast
Questions and Answers
What is the general form of a linear equation with n variables?
What is the general form of a linear equation with n variables?
- $a_{1}x_{1}+ ldots +a_{n}x_{n}=0$
- $a_{1}x_{1}+ ldots +a_{n}x_{n}+b=0$ (correct)
- $a_{1}x_{1}+ ldots +a_{n}x_{n}=b$
- $a_{1}x_{1}+ ldots +a_{n}x_{n}-b=0$
What condition must be satisfied for a meaningful linear equation?
What condition must be satisfied for a meaningful linear equation?
- The coefficients $a_1, ..., a_n$ can be any real numbers
- The coefficients $a_1, ..., a_n$ must not all be zero (correct)
- The coefficients $a_1, ..., a_n$ can be arbitrary expressions
- The coefficients $a_1, ..., a_n$ must be positive
How can the solutions of a linear equation in two variables be interpreted geometrically?
How can the solutions of a linear equation in two variables be interpreted geometrically?
- As vectors in three-dimensional space
- As Cartesian coordinates of points in the Euclidean plane (correct)
- As angles between lines in the Euclidean plane
- As distances between points in the Euclidean plane
What does the solution of a linear equation represent in the case of one variable?
What does the solution of a linear equation represent in the case of one variable?
What geometric object do the solutions of a linear equation in two variables form?
What geometric object do the solutions of a linear equation in two variables form?
What is the general form of a linear equation with n variables?
What is the general form of a linear equation with n variables?
What do the solutions of a linear equation in two variables form geometrically?
What do the solutions of a linear equation in two variables form geometrically?
What does the solution of a linear equation represent in the case of one variable?
What does the solution of a linear equation represent in the case of one variable?
What condition must be satisfied for a meaningful linear equation?
What condition must be satisfied for a meaningful linear equation?
How can the solutions of a linear equation in two variables be interpreted geometrically?
How can the solutions of a linear equation in two variables be interpreted geometrically?
