Linear Equations Quiz
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Questions and Answers

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?

  • 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?

  • 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?

    <p>Exactly one solution, provided that $a_1 \neq 0$</p> Signup and view all the answers

    What geometric object do the solutions of a linear equation in two variables form?

    <p>A line in the Euclidean plane</p> Signup and view all the answers

    What is the general form of a linear equation with n variables?

    <p>$a_{1}x_{1}+ ldots +a_{n}x_{n}+b=0$</p> Signup and view all the answers

    What do the solutions of a linear equation in two variables form geometrically?

    <p>A line</p> Signup and view all the answers

    What does the solution of a linear equation represent in the case of one variable?

    <p>Exactly one value that satisfies the equation</p> Signup and view all the answers

    What condition must be satisfied for a meaningful linear equation?

    <p>$a_{1}, ldots, a_{n}$ are required to not all be zero</p> Signup and view all the answers

    How can the solutions of a linear equation in two variables be interpreted geometrically?

    <p>As Cartesian coordinates of points in the Euclidean plane</p> Signup and view all the answers

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