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Tutors Answer Your Questions about Matrices-and-determiminant (FREE)
Question 391924: Given the linear system
3x+4y=s
6x+8y=t
(a)determine particular values for s and t so that the system is consistent.
(b)determine particular values for s and t so that the system is inconsistent.
(c)what relationship between the values of s and t will guarantee that the system is consistent?
Click here to see answer by robertb(5830)   |
Question 391931: Determine a solution to each of the following linear systems, using the fact that Ax=b is consistent if and only if b is a linear combination of the columns of A:
{1234/2341/3412}{A/B/C/D}={20/20/20}
(Hints:It is {4x3 matrix}{4x1 matrix}={3x1 matrix},slash / mean next row)
P/S:I don't know how to write matrix bracket,hope you will understand
Click here to see answer by stanbon(75887) |
Question 391983: I am stuck with these martix problems! could someone please help? Here is the problem: Use Guassian elimination to find the complete solution to each system of equations, or show that none exists.
Here is the system of equations:
2w-x+3y+z=0
3w+2x+4y-z=0
5w-2x-2y-z=0
2w+3x-7y-5z=0
(It almost looks like all the variables must be "0", but that can't be right!)
Anyway, here is the matrix taken from the system:
2 -1 3 1 0
3 2 4 -1 0
5 -2 -2 -1 0
2 3 -7 -5 0
Ok, I need help from here, please! Thank you to whomever responds!
Click here to see answer by richard1234(7193)  |
Question 392771: Please help! I need to solve the following using Cramer's Rule. The textbook doesn't do a good job of defining this, so i would be extremely grateful for any help!!
solve by Cramer's Rule:
3x=7y+1
2x=3y-1
solve by Cramer's rule:
x-3y+z=-2
x+2y =8
2x-y =1
Thank you for your help!
Click here to see answer by stanbon(75887) |
Question 392769: Could someone please help? I need to a) write each linear equation as a matrix equation in the form of AX=B. then i have to B) solve the system using the inverse that is given for the coefficient matrix.
here is the problem:
The system is:
x-6y+3z=11
2x-7y+3z=14
4x-12y+5z=25
The inverse of: 1 -1 1
0 2 -1
2 3 0
is.... 3 3 -1
-2 -2 1
-4 -5 2
Please help!! I have NO idea where to start! Thank you to whomever responds!!!
Click here to see answer by stanbon(75887) |
Question 392758: Please help!! Am having great difficulty! The problem:
Use the fact that if A= a b
c d , then A^-1 = 1/ad-bc * d -b
-c a
to find the inverse of each matrix, if possible. Check that AA^-1=I2 and
A^-1A=I2.
A= 6 -3
-2 1
Thank you sooo much to whomever responds!
Click here to see answer by jim_thompson5910(35256) |
Question 392754: could someone please help?
I need to solve each system of equations using guassian elimination w/back substitution or guass-jordan elimination. here is the system of equations:
1st system:
3y-z=-1
x+5y-z=-4
-3x+6y+2z=11
2nd system:
3a+b-c=0
2a+3b-5c=1
a-2b+3c=-4
3rd system:
2w-3x+4y+z=7
w-x+3y-5z=10
3w+x-2y-2z=6
Thank you to the person who responds! I would be extremely grateful for your assistance!!!
Click here to see answer by solver91311(24713)  |
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(24713) |
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(7193) |
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(19441)  |
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(75887) |
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(75887) |
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(75887) |
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(75887) |
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(7193) |
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 in finite 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(75887) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645
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