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

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 Algebra: Matrices, determinant, Cramer rule Solvers Lessons Answers archive Quiz In Depth

 Question 64070: A company manufactures three types of wooden chairs; the Kitui, the Goa, and the Santa Fe. To make a Kitui chair requires one hour of cutting time, 1.5 hours of assembly time, and one hour of finishing time. A Goa chair requires 1.5 hours of cutting time, 2.5 hours for assembly, and 2 hours for finishing. The Santa Fe requires 1.5 hours of cutting, 3 hours of assembly, and 3 hours of finishing.If 41 hours of cutting time, 70 hours of assembly, and 58 hours of finishing time were used one week, how many of each type of chair were produced? Click here to see answer by stanbon(57361)

 Question 64185: I need help with making equations out of matrices with x and y? Click here to see answer by venugopalramana(3286)

 Question 64179: x - y + w = -4 -2x + y + z = 8 2x - 2y - z = -10 -2x + z + w = 5 Please solve this system of equations using the reduced row echelon form of the matrix. Click here to see answer by venugopalramana(3286)

 Question 64107: Solve the system if possible. 2x-4y+2z=11 x+3y-2z=-9 4x-2y+z=7 Click here to see answer by ankor@dixie-net.com(15656)

 Question 64327: Solve the system of linear equations by using the matrices: [9,3,4][x1]=7 [4,3,4][x2]=8 [1,1,1][x3]=3 Thank you! Click here to see answer by venugopalramana(3286)

 Question 64626: I have tried for 2 days to solve this one! I have the answers, and they do solve the equations, so they are correct. However, I am unable to produce the answers using matrix transformations. Any step-by-step help would be appreciated. -2r + 6s -3t + 3v = -5 4r - 3s + 2t -v = -3 -3r - 4s - 3t + 4v = -15 5r + 2s - 2t + 3v = -20 The solution is r,s,t,v = -2,1,3,-2 respectively. Click here to see answer by venugopalramana(3286)
 Question 64626: I have tried for 2 days to solve this one! I have the answers, and they do solve the equations, so they are correct. However, I am unable to produce the answers using matrix transformations. Any step-by-step help would be appreciated. -2r + 6s -3t + 3v = -5 4r - 3s + 2t -v = -3 -3r - 4s - 3t + 4v = -15 5r + 2s - 2t + 3v = -20 The solution is r,s,t,v = -2,1,3,-2 respectively. Click here to see answer by Fermat(127)

 Question 64640: during a race a high performance sailboat traveled 54 miles with the wind in 3 hours. the return trip, against the wind, took 6 hours. find the rate of the boat in calm water and the rate of the wind Click here to see answer by ptaylor(2048)

 Question 65004: How do you raise a matrix equation by a negative number? Click here to see answer by stanbon(57361)

 Question 65225: I need super fast help! Use Gaussian elimination to solve the system: x-3z=-2 3x+y-2z=5 2x + 2y + z=4 After working through it, the numbers dont seem to fit. I have no idea what im doing wrong. I came up with 1 0 -3 -2 0 1 -5.5 -1 0 0 1 3.5 but when I plug the numbers in, they dont fit the equation. I dont know at what step I went wrong and my work is due tomorrow! Please help! Click here to see answer by stanbon(57361)

 Question 65283: If (5,6) IS ON A LINE WITH THE SLOPE OF 4/3, GIVE THE COORDINATES FOR ANOTHER POINT ON THE LINE. Click here to see answer by ptaylor(2048)

 Question 65300: What's the determinant of {6 0}? {3 4} Click here to see answer by funmath(2925)

 Question 65472: This is a word problem question that has to be solved using cramers rule At a college basketball game, student tickets cost 12 dollars each, adult tickets cost 16 dollars each and childrens tickets cost 7 dollars each. Four times as many adult tickets as children tickets were sold, the total number of childrens tickets and adult tickets was half the number of student tickets. The total number of tickets sales was 33,043 dollars. How many of each type of ticket was sold? Click here to see answer by Edwin McCravy(8909)
 Question 65472: This is a word problem question that has to be solved using cramers rule At a college basketball game, student tickets cost 12 dollars each, adult tickets cost 16 dollars each and childrens tickets cost 7 dollars each. Four times as many adult tickets as children tickets were sold, the total number of childrens tickets and adult tickets was half the number of student tickets. The total number of tickets sales was 33,043 dollars. How many of each type of ticket was sold? Click here to see answer by venugopalramana(3286)

 Question 65310: can you help me solve for x and y [3 4y] = [ 3 2] 5 8 2x-1 8 i tried and i got this, 3+4y=3 -4 -4 3y=-1 - - 3 3 y=-1/3 Click here to see answer by venugopalramana(3286)

 Question 64106: Use Gaussian elimination with backward substitution to solve the system of linear equations. Write the solution as an ordered pair or ordered triple, whenever possible. x+2y+z=3 x+y-z=3 -x-2y+z=-5 Click here to see answer by venugopalramana(3286)

 Question 64639: find an equation in the form y=ax^2+bx+c whose graph passes through the points (-1,-2), (1,4), (2,13) Click here to see answer by venugopalramana(3286)

 Question 65872: I need help with Matrix and the directions in the book say "Find the product. If it is not defined, state the reason. The matrix is [7.3 1.5 1.8 0 [-4.2 2.6 -8.7] 2.9 3.2] Click here to see answer by Edwin McCravy(8909)

 Question 66250: ```Solve the linear system using the given inverse of the coefficent matrix. w + 6x + 3y - 3z = 2 2w + 7x + y + 2z = 5 w + 5x + 3y - 3z = 3 - 6x - 2y + 3z = 6 A-1 = Do I plug in the number from the inverse coefficent matrix into the linear system, and then possibly use Cramer's Rule?``` Click here to see answer by Edwin McCravy(8909)

 Question 67773: PLEASE HELP ME ANSWER THIS QUESTION,I'M GOING TO TAKE A TEST ON THURSDAY ON PROBLEMS SIMILAR TO THIS ONE AND I DON'T GET IT!!! CONSIDER THE SYSTEM OF EQUATIONS. 9X+3Y+Z=10 25X+5Y+Z=36 4X-2Y+Z=15 a) REWRITE THIS SYSTEM AS A MATRIX EQUATION. Click here to see answer by stanbon(57361)

 Question 69216: ```(x 3)=2(x 2) solve for x (4 x)= (1 3) on each side of the equals sign is one matrix not two separate matices.``` Click here to see answer by Edwin McCravy(8909)

 Question 69829: Can u please check & tell me if my answer is wrong or not? Given: C= (matrix(2,2,-3,4,2,5)) B= (matrix(3,2,3,-6,5,7,-4,6)) Question: 3CB What i've tried: 3(matrix(2,2,-3,4,2,5))* (matrix(3,2,3,-6,5,7,-4,6)) consider them as 4 vertically aligned matrix symbols: = 3[-3 4]*[3 -6 5] [2 5] [7 -4 6] = 3[ (-3*3+4*7) (-3*-6+4*-4) (-3*5+4*6) ] [ (2*3+5*7) (2*-6+5*-4) (2*5+5*6) ] = 3 [ (-9+28) (18-16) (-15+24) ] [ (6+35) (-12-20) (10+30) ] = 3 [19 2 8] [41 -32 40] = [ 3*19 3*2 3*8 ] [ 3*41 3*-32 3*40] = [57 6 24] [123 -96 120] Final result- (matrix(3,2,57,6,24,123,-96,120)) Click here to see answer by venugopalramana(3286)

 Question 70442: Hello. I have just started a new math class, and the teacher is very hard to understand. When someone asks him a question, he thinks they are making fun of his accent. I am trying to a few things out but cannot. He gives us sample problems and does not even go out of a book. The problem directions are Find A-1 and check your answer. The problem is A= (1 -2 3) (-1 0 2) (4 1 5) Could someone show me the formula for this problem, and perhaps lead me through it? I am lost and do not want to drop this class. Thanks in advance. Click here to see answer by venugopalramana(3286)

 Question 73000: I'm in an algebra two class and I don't understand one bit of it. When I do finally comprehend, my teacher confuses me. Help! He gave us homework to do and the whole class has decided to omit it. I don't want to. I need to understand this stuff. So can someone please help me? It's due monday. I just need an example so I can try to figure out how to do the rest. Here's the problem... Calculate the determinant of the matrix. [18 5] 9 -4 Click here to see answer by stanbon(57361)

 Question 73109: I don't know if I am on the right track or not , and I am not sure how to finish. 2 [1 -9] [0 -2 -8] - [1 10 6] [4 3] [4 7 5] - [5 -2 0] The brackets are to go around both rows (It is 2 times a 2by2 times a 2by3 subtract a 2by3 I have 2[-36 -65 -53] - [1 10 6] [ 12 13 -17] - [5 -2 0] I am not sure how to do the rest, do I multiply 2 by each # in the first 2x3? Please help. Click here to see answer by stanbon(57361)

 Question 73110: Hi! I am having trouble with writing determinants and understanding Cramer's Rule. Please help me! This is one of my practice questions. There are a few like this so I am hoping if you show me how to do this one, I will be able to do the rest of them myself. Thanks! Cramer's Rule is used to solve the system of equations: 3x-y+2z=17, 4x+2y-3z=10, and 2x+5y-9z=-6. Write a determinant to represent the numerator for z. Click here to see answer by stanbon(57361)

 Question 73134: can you also help me solve this system using Cramer's rule?... s + p + c = 40 c = 4p s = p - 2 Click here to see answer by bucky(2189)

 Question 73125: can you help me write this system as a matrix equation and solve using an inverse matrix please?... s + p + c = 40 c = 4p s = p - 2 Click here to see answer by stanbon(57361)

 Question 73181: Solve by either elimination, substitution or Crammer's Rule. I am not sure how to do this problem since there is more than one # on the right side of the =. Please help. y=10-2z-x 4x-y=2 -5+5z=4x+3y Click here to see answer by stanbon(57361)

 Question 73188: Help! I don't know if I'm doing this right. Use the matrix method. x+y-z = -9 2x-y-2z=-3 x+2y+3z=14 I'm confused I seen one way adding R1+R3 to start and another saying interchange row 1 and 3????? This is what I have done: R1 1 1 -1 | -9 R2 2 -1 -2 | -3 R3 1 2 3 | 14 R1 1 2 3 | 14 R2 2 -1 -2 | -3 R3 1 1 -1 | -9 R1 1 2 3 | 14 R2 0 -5 -8 |-31 R3 1 1 -1 | -9 R1 1 2 3 | 14 R2 0 -5 -8 |-31 R3 0 -1 -4 |-23 R1 1 2 3 | 14 R2 0 1 8/5 | 31/5 R3 0 -1 -4 |-23 ?????????????????????????????????? Click here to see answer by stanbon(57361)

 Question 73203: What is the product of this matrix equation using inverse matrices? [3 -4 x [a = [6 2 1] x b] = 7] (That is supposed to be a 2x2, a 1x1, and another 1x1. I put the equal and multiplication signs on both top and bottom to make the matrices look a little more aligned.) Thank you! Click here to see answer by stanbon(57361)

 Question 73960: Solve for x: [2x 5]=[x 0 1] [1 3]=[2 -2 4] =[5 3 1] theres only two matrices. 1 on each side of the equal side Click here to see answer by Edwin McCravy(8909)

 Question 74871: This is actually a total value problem using a graph. How many lbs. of whole milk and cream should be mixed to form 200lbs for cream cheese. whole milk= 4% milk fat, milk for cream cheese = 8 % milk fat and cream =30% milk fat. Click here to see answer by stanbon(57361)

 Question 76542: I need help I don't know how to set it up. Don't know what to do. This problem is from texbook. Fill 10 gallons of premium gas and a small gas can with 2 gallons of regular gas. You pay \$13.56. The price of premium gas is 12 cents more per gallon than theprice per gallon for regular gas. regular 2 gal. can premium 10 gal. for car = \$13.56 Click here to see answer by checkley75(3666)