Lesson test: Two equations, and then two thousand

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Two equations, and then two thousand

1.[1p]
Which of these equations is linear in $x$ and $y$ ?

$7 x - 2 y = - 1$

Correct

$x y + 3 = 0$

The answer is: $7x - 2y = -1$

$x^{2} + y = 4$

The answer is: $7x - 2y = -1$

$\sin x + y = 0$

The answer is: $7x - 2y = -1$

2.[2p]
Which operations may be applied to a system without changing its solutions?

Select all that apply

Multiplying an equation by a non-zero number

Correct

Adding a multiple of one equation to another

Correct

Swapping two equations

Correct

Multiplying an equation by zero

The answer is: Multiplying an equation by a non-zero number, Adding a multiple of one equation to another, Swapping two equations

3.[2p]
Solve $2 x + y = 5$ and $x - 3 y = - 1$ . What is $x$ ?

CorrectNot quite: 2

4.[1p]
A system of linear equations can have exactly two solutions.

True

The answer is: False

False

Correct

5.[3p]
Match the final line reached by elimination to what it means.

0 = -1
0 = 0
z = -1
0.5y + 0.5z = 1

a unique solution
infinitely many solutions
no solution
a step still to back substitute

Show the answer

0 = -1: no solution 0 = 0: infinitely many solutions z = -1: a unique solution 0.5y + 0.5z = 1: a step still to back substitute

6.[2p]
Using $n^{3} / 3$ , about how many multiplications does elimination need for $n = 300$ ? Give the answer in millions.

CorrectNot quite: 9

7.[2p]
Why is Cramer's rule not used as an algorithm for large systems?

The naive determinant cost grows like $n!$ , which is $2.4 \times 10^{18}$ operations at $n = 20$

Correct

It gives the wrong answer when the system is inconsistent

The answer is: The naive determinant cost grows like $n!$, which is $2.4 \times 10^{18}$ operations at $n = 20$

It only works for systems of two equations

The answer is: The naive determinant cost grows like $n!$, which is $2.4 \times 10^{18}$ operations at $n = 20$

It requires the coefficients to be whole numbers

The answer is: The naive determinant cost grows like $n!$, which is $2.4 \times 10^{18}$ operations at $n = 20$

8.[2p]
Put the stages of solving a three by three system in the order they are carried out.

Back substitute upward to recover the remaining unknowns
Use the new second equation to remove the second unknown from the third
Read the last unknown off the final equation
Use the first equation to remove the first unknown from the other two

Show the answer

a, b, c, d

9.[2p]
What one word describes a system whose equations contradict each other?

CorrectNot quite: inconsistent

1.[1p] Which of these equations is linear in x and y?

2.[2p] Which operations may be applied to a system without changing its solutions?

3.[2p] Solve 2x+y=5 and x-3y=-1. What is x?

4.[1p] A system of linear equations can have exactly two solutions.

5.[3p] Match the final line reached by elimination to what it means.

6.[2p] Using n3/3, about how many multiplications does elimination need for n=300? Give the answer in millions.

7.[2p] Why is Cramer's rule not used as an algorithm for large systems?

8.[2p] Put the stages of solving a three by three system in the order they are carried out.

9.[2p] What one word describes a system whose equations contradict each other?

1.[1p]
Which of these equations is linear in $x$ and $y$ ?

2.[2p]
Which operations may be applied to a system without changing its solutions?

3.[2p]
Solve $2 x + y = 5$ and $x - 3 y = - 1$ . What is $x$ ?

4.[1p]
A system of linear equations can have exactly two solutions.

5.[3p]
Match the final line reached by elimination to what it means.

6.[2p]
Using $n^{3} / 3$ , about how many multiplications does elimination need for $n = 300$ ? Give the answer in millions.

7.[2p]
Why is Cramer's rule not used as an algorithm for large systems?

8.[2p]
Put the stages of solving a three by three system in the order they are carried out.

9.[2p]
What one word describes a system whose equations contradict each other?