Elementary Linear Algebra Chapter 1 Quiz

An equation of the form:

a₁x₁+a₂x₂+ ...+a_nx_n = b

is called a ____________________________________.

• quadratic equation

• homogeneous linear equation

• linear equation

• exponential equation

Given the equation

a₁x₁+a₂x₂+ ...+a_nx_n = b and the condition that b = 0, the equation is called a _____________________________.

• homogeneous linear equation

• system of linear equations

• linear system

• non-homogeneous linear equation

Given a linear system, the variables are called

• answers

• solutions

• unknowns

• equations

Given a general linear system of m equations in the n unknowns, x₁, x₂, ..., x_n, a sequence of n numbers s₁,s₂,s₃, ..., s_n for which x₁=s₁, ..., x_n=s_n makes each equation true, the sequence is: (more than one answer).

• solution

• can be written as (s₁, s₂, ..., s_n)

• ordered n-tuple

• ordered pair

A linear system is consistent if _________________________

• has a few solultions

• has no solutions

• has an infinite number of solutions

• has at least one solution

A linear system is inconsistent if _________________________

• has a few solultions

• has no solutions

• has an infinite number of solutions

• has at least one solution

This is an example of a(n) ______________.

• augmented matrix

• matrix

• invertible matrix

• homogeneous linear system

A free variable in a linear system is one that corresponds to a pivot column in the coefficient matrix.

• True

• False

In the following linear system, determine the value(s) of h and k such that the system has infinite number of solutions. Type h=__,k=__

Do the three planes x₁ +2x₂ +x₃ = 4, x₂ - x₃ = 1, and x₁ +3x₂ = 0 have a common point of intersection?

• Yes. Solution set is y=1+z.

• No. It is inconsistent.

• Yes. Solution set is x = 4-2y-z.