<< Chapter < Page Chapter >> Page >

Section exercises

Verbal

Explain why we can always evaluate the determinant of a square matrix.

A determinant is the sum and products of the entries in the matrix, so you can always evaluate that product—even if it does end up being 0.

Got questions? Get instant answers now!

Examining Cramer’s Rule, explain why there is no unique solution to the system when the determinant of your matrix is 0. For simplicity, use a 2 × 2 matrix.

Got questions? Get instant answers now!

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.

The inverse does not exist.

Got questions? Get instant answers now!

The determinant of 2 × 2 matrix A is 3. If you switch the rows and multiply the first row by 6 and the second row by 2, explain how to find the determinant and provide the answer.

Got questions? Get instant answers now!

Algebraic

For the following exercises, find the determinant.

| 2 3 3.1 4 , 000 |

7 , 990.7

Got questions? Get instant answers now!

| 1.1 0.6 7.2 0.5 |

Got questions? Get instant answers now!

| 1 0 0 0 1 0 0 0 3 |

3

Got questions? Get instant answers now!

| 1 4 0 0 2 3 0 0 3 |

Got questions? Get instant answers now!

| 1 0 1 0 1 0 1 0 0 |

1

Got questions? Get instant answers now!

| 2 3 1 3 4 1 5 6 1 |

Got questions? Get instant answers now!

| 2 1 4 4 2 8 2 8 3 |

224

Got questions? Get instant answers now!

| 6 1 2 4 3 5 1 9 1 |

Got questions? Get instant answers now!

| 5 1 1 2 3 1 3 6 3 |

15

Got questions? Get instant answers now!

| 1.1 2 1 4 0 0 4.1 0.4 2.5 |

Got questions? Get instant answers now!

| 2 1.6 3.1 1.1 3 8 9.3 0 2 |

17.03

Got questions? Get instant answers now!

| 1 2 1 3 1 4 1 5 1 6 1 7 0 0 1 8 |

Got questions? Get instant answers now!

For the following exercises, solve the system of linear equations using Cramer’s Rule.

2 x 3 y = −1 4 x + 5 y = 9

( 1 , 1 )

Got questions? Get instant answers now!

5 x 4 y = 2 4 x + 7 y = 6

Got questions? Get instant answers now!

   6 x 3 y = 2 8 x + 9 y = −1

( 1 2 , 1 3 )

Got questions? Get instant answers now!

2 x + 6 y = 12 5 x 2 y = 13

Got questions? Get instant answers now!

4 x + 3 y = 23    2 x y = −1

( 2 , 5 )

Got questions? Get instant answers now!

10 x 6 y = 2 5 x + 8 y = −1

Got questions? Get instant answers now!

4 x 3 y = −3 2 x + 6 y = −4

( 1 , 1 3 )

Got questions? Get instant answers now!

4 x 5 y = 7 3 x + 9 y = 0

Got questions? Get instant answers now!

4 x + 10 y = 180 3 x 5 y = −105

( 15 , 12 )

Got questions? Get instant answers now!

   8 x 2 y = −3 4 x + 6 y = 4

Got questions? Get instant answers now!

For the following exercises, solve the system of linear equations using Cramer’s Rule.

     x + 2 y 4 z = 1    7 x + 3 y + 5 z = 26 2 x 6 y + 7 z = 6

( 1 , 3 , 2 )

Got questions? Get instant answers now!

5 x + 2 y 4 z = 47      4 x 3 y z = 94     3 x 3 y + 2 z = 94

Got questions? Get instant answers now!

     4 x + 5 y z = −7 −2 x 9 y + 2 z = 8            5 y + 7 z = 21

( 1 , 0 , 3 )

Got questions? Get instant answers now!

4 x 3 y + 4 z = 10 5 x 2 z = 2 3 x + 2 y 5 z = 9

Got questions? Get instant answers now!

4 x 2 y + 3 z = 6       6 x + y = 2 2 x + 7 y + 8 z = 24

( 1 2 , 1 , 2 )

Got questions? Get instant answers now!

5 x + 2 y z = 1 7 x 8 y + 3 z = 1.5 6 x 12 y + z = 7

Got questions? Get instant answers now!

   13 x 17 y + 16 z = 73 11 x + 15 y + 17 z = 61    46 x + 10 y 30 z = 18

( 2 , 1 , 4 )

Got questions? Get instant answers now!

4 x 3 y 8 z = 7    2 x 9 y + 5 z = 0.5    5 x 6 y 5 z = 2

Got questions? Get instant answers now!

   4 x 6 y + 8 z = 10 2 x + 3 y 4 z = 5           x + y + z = 1

Infinite solutions

Got questions? Get instant answers now!

4 x 6 y + 8 z = 10 2 x + 3 y 4 z = 5 12 x + 18 y 24 z = 30

Got questions? Get instant answers now!

Technology

For the following exercises, use the determinant function on a graphing utility.

| 1 0 8 9 0 2 1 0 1 0 3 0 0 2 4 3 |

24

Got questions? Get instant answers now!

| 1 0 2 1 0 −9 1 3 3 0 −2 −1 0 1 1 −2 |

Got questions? Get instant answers now!

| 1 2 1 7 4 0 1 2 100 5 0 0 2 2,000 0 0 0 2 |

1

Got questions? Get instant answers now!

| 1 0 0 0 2 3 0 0 4 5 6 0 7 8 9 0 |

Got questions? Get instant answers now!

Real-world applications

For the following exercises, create a system of linear equations to describe the behavior. Then, calculate the determinant. Will there be a unique solution? If so, find the unique solution.

Two numbers add up to 56. One number is 20 less than the other.

Yes; 18, 38

Got questions? Get instant answers now!

Two numbers add up to 104. If you add two times the first number plus two times the second number, your total is 208

Got questions? Get instant answers now!

Three numbers add up to 106. The first number is 3 less than the second number. The third number is 4 more than the first number.

Yes; 33, 36, 37

Got questions? Get instant answers now!

Three numbers add to 216. The sum of the first two numbers is 112. The third number is 8 less than the first two numbers combined.

Got questions? Get instant answers now!

For the following exercises, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.

You invest $10,000 into two accounts, which receive 8% interest and 5% interest. At the end of a year, you had $10,710 in your combined accounts. How much was invested in each account?

$7,000 in first account, $3,000 in second account.

Got questions? Get instant answers now!

Questions & Answers

given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Practice Key Terms 2

Get the best College algebra course in your pocket!





Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask