Question 1

Determine which of the points (2, -3), (2, 3), and (4, 2) lie on both of the lines 
  and 
  
.

Accepted Answer

(2, 3)

Question 2

Determine which of the points (1, 0, -1, 0), (0, 1, 2, 3), and (2, 1, -1, -1) satisfy the linear system

Accepted Answer

(0, 1, 2, 3)

Question 3

Determine which of (3, s₂, s₁, 2), (0, 0, 0 ,0), (2 - s₁ - s₂, 1 + s₁ + s₂, s₁, s₂), and (3 - s₁, s₁, s₂, 2 - s₂) form a solution to the following system for all choices of the free parameters .

Accepted Answer

(2 - s₁ - s₂, 1 + s₁ + s₂, s₁, s₂)

Question 4

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Accepted Answer

The answer of Determine if the system is in echelon...

Question 5

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Accepted Answer

The answer of Determine if the system is in echelon...

Question 6

Find all solutions to the system

Accepted Answer

The answer of Find all solutions to the system
 ...

Question 7

Find all solutions to the system

Accepted Answer

The answer of Find all solutions to the system
 ...

Question 8

Find all solutions to the system

Accepted Answer

The answer of Find all solutions to the system
 ...

Question 9

Reorder the equations to put the following system of three equations with four unknowns in echelon form:
  ​

Accepted Answer

The answer of Reorder the equations to put the following...

Question 10

Determine the value(s) of 
  so that the following system is consistent.​

Accepted Answer

The answer of Determine the value(s) of 
  so...

Question 11

Suppose a system of 
  equations has two free variables. How many leading variables are there?

Accepted Answer

The answer of Suppose a system of 
  equations...

Question 12

If a linear system has more variables than equations, then the system is inconsistent.

Accepted Answer

If the system has more variables than equations, it may have infinitely many solutions or be inconsistent, but it is not always true that it is inconsistent. The type of solution will depend on the specific equations and variables involved.

Question 13

If a linear system has infinitely many solutions, then there are more variables than equations.

Accepted Answer

A linear system can have infinitely many solutions if at least one equation is a linear combination of the others, indicating the system is dependent, not necessarily because there are more variables than equations.

Question 14

If a linear system has no free variables, then there exists at most one solution.

Accepted Answer

If a linear system has no free variables, then it can be uniquely solved using elimination or other methods. Therefore, there can be at most one solution.

Question 15

Convert the augmented matrix to the equivalent linear system.

Accepted Answer

The answer of Convert the augmented matrix to the equivalent...

Question 16

Convert the augmented matrix to the equivalent linear system.

Accepted Answer

The answer of Convert the augmented matrix to the equivalent...

Question 17

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Accepted Answer

The answer of Determine whether the matrix is in reduced...

Question 18

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Accepted Answer

The answer of Determine whether the matrix is in reduced...

Question 19

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Accepted Answer

The answer of Determine whether the matrix is in reduced...

Question 20

Identify the row operation which transforms the matrix on the left to the matrix on the right.

Accepted Answer

The answer of Identify the row operation which transforms the...

Quiz 1: Systems of Linear Equations

Determine which of the points (2, -3), (2, 3), and (4, 2) lie on both of the lines and .

Determine which of the points (1, 0, -1, 0), (0, 1, 2, 3), and (2, 1, -1, -1) satisfy the linear system

Determine which of (3, s2, s1, 2), (0, 0, 0 ,0), (2 - s1 - s2, 1 + s1 + s2, s1, s2), and (3 - s1, s1, s2, 2 - s2) form a solution to the following system for all choices of the free parameters .

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Find all solutions to the system

Find all solutions to the system

Find all solutions to the system

Reorder the equations to put the following system of three equations with four unknowns in echelon form: ​

Determine the value(s) of so that the following system is consistent.​

Suppose a system of equations has two free variables. How many leading variables are there?

If a linear system has more variables than equations, then the system is inconsistent.

If a linear system has infinitely many solutions, then there are more variables than equations.

If a linear system has no free variables, then there exists at most one solution.

Convert the augmented matrix to the equivalent linear system.

Convert the augmented matrix to the equivalent linear system.

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Identify the row operation which transforms the matrix on the left to the matrix on the right.

Determine which of (3, s₂, s₁, 2), (0, 0, 0 ,0), (2 - s₁ - s₂, 1 + s₁ + s₂, s₁, s₂), and (3 - s₁, s₁, s₂, 2 - s₂) form a solution to the following system for all choices of the free parameters .

Reorder the equations to put the following system of three equations with four unknowns in echelon form:

Determine the value(s) of so that the following system is consistent.