Questions on Algebra: Matrices, determinant, Cramer rule answered by real tutors!

Tutors Answer Your Questions about Matrices-and-determiminant (FREE)

Question 393288: Joe is selling tickets to the annual pancake breakfast. On the first day of tickets sales the school sold 3 senior citizen tickets and 5 child tickets for a total of $70. The school took in $216 on the second day by selling 12 senior citizen tickets and 12 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
3s+5c=70
12s+12c=216
That is as far as I got. I'm not sure where to go from there. Thank you in advance for your time and help.
Click here to see answer by solver91311(16872)

Question 393527: 2a-3b=-8
4a+3b=-34
I am supposed to be using either substitution, elimination, or inverse matrices to solve.
Thanks in advance for your time and help!
Click here to see answer by stanbon(57282)

Question 393517: A) Graph the system
B) Tell how many solutions the system has
C) Estimate the solution(s)
y=2x+2
y=-2x+6
My teacher said something about multiplying by zero, but I'm not sure if that was for a different graphing problem. I'm very confused...
Thanks in advance for your time and help.
Click here to see answer by richard1234(5390)

Question 393585: solve for x,
[-5 0 -1]
[2 1 0] = 4
[x 3 0]
Click here to see answer by robertb(4012)

Question 393686: solve :
[1 0 -5]
2[5 -2 1]
[2 3 1]
Click here to see answer by Alan3354(30993)

Question 393858: 3n+6(n-12) is greater than or equal to 9
Solve the inequality and graph its solution set.
I'm not sure how to get this problem solved...
Thanks in advance for your time and help!
Click here to see answer by josmiceli(9664)

Question 393885: concert tickets cost $24 an adult, $15 a child, and $12 a senior, If they made $5670 dollars, and 5 times as many adults attended as seniors, and 2 times as many children attended then seniors, how could i set up a system of equations ,and find how much of each ticket was sold?
Click here to see answer by josmiceli(9664)

Question 394532: simplify 3[2-(4-x)+7]
Click here to see answer by edjones(7569)

Question 395394: I could definitely use help with the following: Solve the following system of equations using matrices and guassian or gauss-jordan elimination. Here is the system of equations:
3a+b-c=0
2a+3b-5c=1
a-2b+3c=-4
My augmented matrix is:
3 1 -1 0
2 3 -5 1
1 -2 3 -4

I swapped R3 and R1->R1
1 -2 3 -4
2 3 -5 1
3 1 -1 0
Now I'm stuck. Could a tutor please help? Thank you very much!
Click here to see answer by stanbon(57282)

Question 395476: 1.5x+y7=-3
2x+3y=-1
2.2x+3y=7
8x+12y=2
3.2x-y+3z=9
x+2z=3
3x+2y+z=10
I am supposed to solve these problems using cramer's rule and i have no idea how to set it up or what the steps are to solving the problems. Can you please help me

Click here to see answer by stanbon(57282)

Question 395667: Use Cramer's Rule to solve each system or determine that the system is inconsistent or contains dependent equations
The system is:
3x=7y+1
2x=3y-1
Thank you! I would appreciate any help!
Click here to see answer by ewatrrr(10682)

Question 395961: i need to solve these two systems of equations: 3x+4y=12 and 2x+y=13
we have to solve these equations using: graphing, substitution, elimination, matrix and the cramers rule methods.
i know that all the answers will be the same, and when i worked out this problem according to the elimination method i got the point of intersection as (-8,9) but when i was trying to graph it i was getting weird numbers and couldn't set up the graph.
-thanks so much if you could help me out :) kristianne
Click here to see answer by stanbon(57282)

Question 397660: I dont really quite get how to solve augmented matrices by hand,I can do simple ones but some are really hard, this is the one I am stuck on,can you please show me step by step.
a+b-c=6
2a+b+c=-10
a+4b-3c=9
Click here to see answer by stanbon(57282)

Question 397526: Find the values of b and c for which the equations x+5y=4 and 2x+by=c have:
A unique solution, an infinite set of solutions and no solution.
Click here to see answer by robertb(4012)

Question 397775: Dear sir, i got stuck on this home work problem, please help me
"If u = −2i + 4j, v = 3i + 2j, w = 4i + 6j then |u + v + w| is
a) 5
b) 13
c) 4
d) 15
Click here to see answer by robertb(4012)

Question 397771: Hai sir,
Pls help on this problem
"An idempotent matrix A where
a) A2 = A
b) A2 = I
c) A2 = -A
d) A2 = 0
Click here to see answer by robertb(4012)

Question 397966: 8. Solve the system using Gauss-Jordan elimination.
-12x1 - 4x2 = -20
3x1 + x2 = -5
x1 = -4, x2 = 6
x1 = -3, x2 = 7
x1 = -4, x2 = 7
No solution

9. Solve the system using Gauss-Jordan elimination.
-x1 + x2 - x3 = 5
x1 + x2 + 4x3 = -1
-3x1 + x2 + x3 = 11
x1 = -3, x2 = 2, x3 = 0
x1 = -3, x2 = 2, x3 = 1
x1 = -2, x2 = 1, x3 = 1
No solution

10. Write the system as a matrix equation and solve using inverses.
x1 + 2x2 - x3 = -3
-2x1 - x2 + 3x3 = 0
-4x1 + 4x2 - x3 = -12
x1 = 2, x2 = -3, x3 = 1
x1 = 1, x2 = -2, x3 = 1
x1 = 1, x2 = -2, x3 = 0
x1 = 1, x2 = -3, x3 = 1
12. Solve the system.
x2 + y2 = 4
y - x = 2
(0, 2), (2, 0)
(0, 2), (-2, 0)
(0, -2), (2, 0)
(0, -2), (-2, 0)

13. Solve the system.
3x2 - 2y2 = -5
x2 + y2 = 25
(3, 4), (3, -4), (-3, 4), (-3, -4)
(4, 4), (5, 4), (3, -4), (1, –4)
(-3, 4), (1, 4), (-3, -4), (2, -4)
(1, 4), (2, –4), (–4, 3), (–3, –3)

14. Find the coordinates of the corner points using the following:
x - y = -2
2x + y = -1
x = -2
(-2, 0)
(-2, 0), (-1, 1)
(-2, 0), (-1, 1), (-2, 3)
(-1, 1), (-2, 3)
15. Esther wants to spend no more than $60 buying gifts for her friends Barb and Wanda. She wants to spend at least $20 on Wanda's gift.
Let B represent the amount Esther spends on Barb's gift and W represent the amount she spends on Wanda's gift. Write a system of linear inequalities that models the information.
B + W < 60
B < 20
W > 0
B + W > 60
B < 20
W > 20
B + W < 60
B > 0
W > 20
B + W > 60
B > 0
W > 20

16. 2x + y < 20
x + 3y < 30
x, y > 0
Maximize z = 3x + 12y subject to the region.
Maximum value of 114 at (6, 8)
Maximum value of 60 at (20, 0)
Maximum value of 120 at (0, 10)
Maximum value of 30 at (10, 0)

17. 2x + y > 14
x + 3y < 12
x, y > 0
Minimize z = 3x + 5y subject to the given region.
Minimum value of 20 at (0, 4)
Minimum value of 21 at (7, 0)
Minimum value of 28 at (6, 2)
Minimum value of 36 at (12, 0)

18. x + 2y < 18
x + y < 10
2x + y < 18
x, y > 0
Maximize z = 3x + 4y subject to the given region.
Maximum value of 42 at (6, 6)
Maximum value of 38 at (2, 8)
Maximum value of 36 at (0, 9)
Maximum value of 32 at (8, 2)

19. x + 2y < 18
x + y > 10
2x + y < 18
x, y > 0
Minimize z = 3x + 5y subject to the given region.
Minimum value of 27 at (9, 0)
Minimum value of 45 at (0, 9)
Minimum value of 34 at (8, 2)
Minimum value of 0 at (0, 0)

Click here to see answer by richard1234(5390)

Question 397873: Could tutor please help with this problem? Help would be greatly appreciated!
Use Cramer's Rule to solve the system.
x-3y+z=-2
x+2y =8
2x-y =1
Thank you for your help!
Click here to see answer by Tatiana_Stebko(1326)

Question 398712: Hello,
I have linear equation problem that I am stuck on. I have tried the problem myself but I'm having trouble with it. Here is the problem I'm working on:
Determine the necessary conditions on a, b and c for the following systems to have:
a unique solution; an infinite number of solutions; or be inconsistent.
x1 + ax2 = 5
3x1 + 6x2 = b
Here is the work I've done so far, and this is all in matrices so imagine the boxes around the numbers:
1 a |5
3 6 |b
multiplying row 2 by 1/3
1 a | 5
1 2 | b/3
subtracting row 1 from row 2
1 a |5
0 2-a |b/3 - 5
I'm not sure if what I've done is correct, but this is where I'm stuck because I do not know how to set up the three conditions?
Thank you for any help
Yury
Click here to see answer by stanbon(57282)

Question 403164: Hello,
I am trying to understand what is required of me in the following two math problems.
1. Modify the second row in the following matrix by adding first row to the second.
2 3 4
-2 1 0
1 3 5
Here is my solution.
(2 + -2) (3+1) (4+0) = 0 4 4
Which makes the final answer,
2 3 4
0 4 4
1 3 5

2. Modify the third row of the following matrix by adding the first row to the third.
1 2 -1
4 1 3
2 1 4
Here is my solution.
(1+2) (2+1) (-1+4) = 3 3 3
Which makes the final answer,
1 2 -1
4 1 3
3 3 3
Is this the correct way to do these problems?
Thank you for any help.

Click here to see answer by scott8148(6628)

Question 404144: CRAMER RULE, ELIMIATION OR SUBSTITUTION METHOD, AND MATRICES PRACTICE PROBLEMS

1. Solve the system using the elimination or substitution method. 5x - 2y = 2; -3x + y = -2

A.
(1, 1)

B.
(-1, -3/2)

C.
(2, 4)

D.
(-2, 4)

2. Solve the system using the elimination or substitution method. x + 4y + z = -6; 3x - 2y - z = -10; 3y + 2z = 4

A.
(3, 2, -4)

B.
(-3, -2, 5)

C.
(1, 0, -2)

D.
(-2, 4, -5)

3. Solve the system using matrices. x + 4y + 2z = -4; 2x - y - z = 10; 2x + 3y + 2z = 2

A.
(3, -2, -1)

B.
(4, -2, 0)

C.
(-2, 5, 3)

D.
(1, -1, 3)

4. Given the cost function C(x) = 2700 + 31x and the revenue function R(x) = 49x, find the number of units that must be old to break even.

A.
150 units

B.
270 units

C.
220 units

D.
310 units

5. Solve the system using matrices. x - y = 1; -8x + 6y = 4

A.
(-5, -6)

B.
(2, 1)

C.
(-2, -1)

D.
(6, 5)

6. Solve the sysyem using Cramer's Rule. 2x - 3y = -13; 7x - 6y = -5

A.
(2, 3)

B.
(7, 9)

C.
(-5, -6)

D.
(-8, -1)

7. Solve the system using matrices. 2x - 8y = 12; x - 4y = -3

A.
(2, -1)

B.
(-3, 0)

C.
No Solution

D.
Infinitely many solutions

8. Solve the system using the elimination or substitution method. x + 2y - 3z = 9; -x + 3y - 2z = 1; 2x - 5y + 2z = 2

A.
(1, -3, 2)

B.
(0, 3, -2)

C.
(6, 3, 1)

D.
(3, 0, -2)

9. Solve the system using the elimination or substitution method. 14x - 7y = -7; 7x + y = 10

A.
(1, 3)

B.
(1, 1)

C.
(-1, -2)

D.
No solution

10. Solve the system using Cramer's rule. 2x + 8y = 11; 8x + 5y = -10

A.
(-3/2, 3)

B.
(-2, 3/2)

C.
(-5/2, 2)

D.
(2, 7/8)

Click here to see answer by richard1234(5390)

Question 404308: I am really struggling with these matrices. If I am using the Gauss-Jordan elimination method then the next row operation for these problems should be?
1. {1 2 -1 | 6}
{0 -2 2 | 6}
{0 2 -4 |-4}
I said R1+R2.
2. {1 1 -1| 6}
{0 -2 2| 6}
(0 2 -4|-4}
I said R1 (-1/2)R2
Please help me to understand the next step to be completed in the Gauss-Jordan elimination method.

Click here to see answer by stanbon(57282)

Question 404790: A factory makes both bicycles and tricycles. Each bicycle has two wheels and three stickers, and each tricycle has three wheels and five stickers. On a recent day, the factory made both bicycles and tricycles. They used 120 wheels and 190 stickers. Hw many bicycles and tricycles were made at the factory that day? All I really need is an equation that I can do the matrices on. I know how to do all the hand work (and have my calculator to check the answer). Any help is very much appreciated!
Click here to see answer by stanbon(57282)

Question 406924: I need help with linear inequalities
6x+5y<123
Click here to see answer by ewatrrr(10682)

Question 408705: solve the system by the substitution method
6x-3y=3
10x=y+7
Click here to see answer by mananth(12270)

Question 409173:
Click here to see answer by Jeef Gorrdon(26)

Question 409498: Use Cramer's Rule to solve the system or to determine that the system is inconsistent or contains dependedent equations.
2x+y=10
6x+3y=30
Click here to see answer by ewatrrr(10682)

Question 409645: Your school sold 456 tickets for a high school play. An adult ticket cost $3.50. A student ticket cost $1. Total ticket sales equaled $1131. Let a equal the number of adult tickets sold, and let s equal the number of student tickets sold. A. Write a system of equation that relates the number of adult and student tickets sold to the total number of tickets sold and to the total ticket sales. B. Solve by elimination to find the number of each type of ticket sold.
Click here to see answer by josmiceli(9664)

Question 411588: Find X, Y, Z: 2X-3Y+ Z=5
X+3Y+8Z=22
3X- Y+2Z=12

Click here to see answer by ewatrrr(10682)

Question 415040: How do I find the dimensions of a matrix product? A3x5 * B5x2
Click here to see answer by robertb(4012)

Question 415184: simplify each expression sqare root of 16
Click here to see answer by ewatrrr(10682)

Question 415746: Good morning,
What steps are necessary in order to solve this system of equations using matrices (row operations).
x + y - z = 6
3x -2y + z =-5
x +3y -2z = 14
1 -1 -1 |6
3 -2 1 |-5
1 -3 -2 |14
Click here to see answer by htmentor(789)

Question 416323: I have a matrix problem where the given is A= and AB = and I have to solve for B. I was told not to divide AB by A. I left my homework at home, I hope someone could please just tell me the first step on where I should start. Thank you!
Click here to see answer by sudhanshu_kmr(1152)

Question 417797: If 7x+5y+6z=55 then y=?
Click here to see answer by MathLover1(6625)

Question 417887: Determine whether the relation is a function.
{(-5, -5), (-1, -2), (1, 8), (1, 2)}

Click here to see answer by Edwin McCravy(8893)

Question 418664: I need help finding the answer if i subtract these 2 matrices. Find A-B.
A={17, 2, 3 / 11, 4,-9} B={10, 6, -7 / -4, 3, 0}
Click here to see answer by ewatrrr(10682)

Question 418922: Find the Product of (2x+4y)(x-3y)
Click here to see answer by rfer(12654)

Question 419050: solve the system of equations using gaussian elimination or gauss-jordan elimination.
1. x-6y=23
2x-6y=28
2. Ellen wishes to mix candy worth $3.44 per pound with candy worth $9.96 per pound to form 24 pounds of a mixture worth $8.33 per pound. How many pounds of the more expensive candy should she use?

Click here to see answer by mananth(12270)

Question 419049: The members of the band were selling t-shirts and school banners for a fundraiser. Justine sold 13 tshirts and 10 banners for a total of $145.00. Carlos sold 15 tshirts and 6 banners for a total of $141.00. How much did the band charge for tshirts? How much for banners?
Click here to see answer by mananth(12270)

Question 421840: Solve each system of equations using the substitution method.
4x - y = 32y = -2 x + 70

Click here to see answer by mananth(12270)

Question 422028: algebracially solve the system of equations. show your work.
ax-by=b+a
bx+ay=b+a
Click here to see answer by jim_thompson5910(28536)

Question 422309: HOW TO SOLVE MENTALY THIS IN 5 SECONDS 68*69
Click here to see answer by ewatrrr(10682)

Question 423165: find the determinant of a. a=4 -7, 3 -2
Click here to see answer by Alan3354(30993)

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