# 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 22280: A machine can produce either nuts or bolts, but not both at the same time. The machine can be used at most 8 hours a day. Furthermore, at most 6 hours a day can be used for making nuts and at most 5 hours a day for making bolts. There is a \$2 profit for each hour the machine makes nuts and a \$3 profit for each hour the machine makes bots. How many hours per day should the machine make each item in order to maximize profit? What is the maximum profit? Please hurry! Click here to see answer by Paul(988)

 Question 22278: Here's the question...A carpentry shop makes dinner tables and coffee tables. Each week the shop must complete at least 9 dinner tables and 13 coffee tables to be shipped to furniture stores. The shop can produce at most 30 dinner tables and coffee tables combined each week. If the shop sells dinner tables for \$120 and coffee tables for \$150, how many of each item should be produced for a maximum weekly income? What is the maximum weekly income?? HELP FAST PLEASE!! I am so desperate right now... Click here to see answer by stanbon(57224)

 Question 22302: ok, so i have absolutly no clue on what to do with this. write each question as a matrix equation. x + y = 5 x - 2y = -4 Click here to see answer by stanbon(57224)

 Question 20235: i have 3 points on a graph that form a triangle and i need to find the area of the triangle using a matrix. How would i find the area? the points are (-2,-2), (3,0), and (2,4). Click here to see answer by khwang(438)

 Question 20108: An example of an invertible 1x1 matrix. An example of a noninvertible 2x2 matrix with 1s on the main diagonal. Click here to see answer by khwang(438)

 Question 22693: This isn't really a question, I just need help on explaining Cramer's Rule. For my essay I have to describe in paragraph form the steps necessary to solve the system of equations using Cramer's Rule. The problem shown is: 2x+y-3z=-3 3x+2y+4z=5 -4x-y+2z=4 Click here to see answer by stanbon(57224)

 Question 22654: Given two n x n matrices A and B where AB=BA how does one show that the determinant of (A^2 + B^2) >=0? Click here to see answer by khwang(438)

 Question 22974: I have been doing very well with matrices, but this one is really giving me a headache. There were two questions on this homework assignment; these instructions apply to both: Evaluate each of the following determinants by expansion by minors. The first problem was a 3x3 matrix. I had no problem with that one. Here's the one that's giving me trouble: -2 3 0 2 3 1 -3 7 -4 5 1 2 6 0 3 -5 Any help you could give would be much appreciated. Thank you in advance. Click here to see answer by stanbon!(97)

 Question 23111: The section we are working on has to do with augmented matrices, and here's the question: "In triangle ABC, the measure of angle A is twice the measure of angle B. The measure of angle C exceeds four times the measure of angle B by 12 degrees. Find the measure of each angle." I've tried this problem several times and just can't find a reasonable answer. Please help. Click here to see answer by rapaljer(4667)

 Question 23151: Let "T" be a linear Operator on a finite dimensional space "V" and let "c" be a Scalar. Then det(T-cI)will be equal to what? Please note that ,I request to let me know the value of Determinant(T-cI).(i mean wheather it is 0,1,2,3 or some other number). Click here to see answer by khwang(438)

 Question 22217: How to find the inverse of a 3X3 matrix without using a calculator? Click here to see answer by stanbon(57224)

 Question 22281: A theater contains 500 seats. For an upcoming talent show, the theater manager plans to sell \$4 and \$5 tickets. He must sell at least 200 \$4 tickets and 100 \$5 tickets for the show to be produced, and he must bring in at least \$2000 to break even. How many tickets at each price should be sold to maximize income? What is the maximum income? Please help me ASAP. Due 1pm Sunday!!! Click here to see answer by stanbon(57224)

 Question 21095: Is there a way to easily solve matrices, 3 system equations, and Cramer's rule problems? What are the short cuts or tricks to solving the above problems? Click here to see answer by venugopalramana(3286)

 Question 23322: I am having a hard time with Matrices and Determinants. Here's the problem I'm having a lot of trouble with: Solve the following system of equations x-2y=5 & -3x+2y=7..... I got x= -6 and y=-11/2, but my test said it was wrong, can anyone explain whats going on here??? Click here to see answer by stanbon(57224)

 Question 23339: How do you find the inverse of something dealing with Matrices abd solutions to systems of linear equations Click here to see answer by stanbon(57224)

 Question 21154: Can you help me to solve this Matrix Transformation problem please? x-2y+3z=3 2x+y+5z=8 3x-y-3z=-22 Thank You Click here to see answer by venugopalramana(3286)

 Question 23986: determinants 2x+y=3 5x+6y=4 [2 1]= 12-5=7 [5 6] x=[3 1] [4 6] then what??? Click here to see answer by venugopalramana(3286)

 Question 24967: How do I find the product of matrices? Click here to see answer by whty89(20)

 Question 25004: What is the order of matrix A? A = [-2 3 4] [1 -5 0] Click here to see answer by stanbon(57224)

 Question 25010: show that the jth column of the matrix product AB is equal to the matrix product ABj, where Bj is the jth column of B Click here to see answer by venugopalramana(3286)

 Question 25009: show that if Ax=b has more than one solution, then it has infinitely many solutions(Hint: If x1 and x2 are solutions, consider x3=rx1 +sx2, where r+s=1) Click here to see answer by venugopalramana(3286)

 Question 24870: Hello! Could you, please, give a hint of how to solve this system of linear equations? I'm at a loss to calculate any determinants here, which is required for most ways of solving, I guess, so I suppose there must be some "face-saver" here. :) The last column is of the coefficients at variables to zero power - I didn't manage to put a line with this formula plotting system. Also the low lines are meant as ellipses. Thank you! Click here to see answer by venugopalramana(3286)
 Question 24870: Hello! Could you, please, give a hint of how to solve this system of linear equations? I'm at a loss to calculate any determinants here, which is required for most ways of solving, I guess, so I suppose there must be some "face-saver" here. :) The last column is of the coefficients at variables to zero power - I didn't manage to put a line with this formula plotting system. Also the low lines are meant as ellipses. Thank you! Click here to see answer by fanks(6)

 Question 26694: Hello!! I'm in algebra 2 and dont understand how to solve this problem regarding Cramer Rule .The problem says:find the inverse of the matrix if it exists [3 -4] [6 -8] Thank you Click here to see answer by longjonsilver(2297)

 Question 26789: X to the power of 7 = 11.49 how do you solve for x Please provide with step by step instructions and also the use of scientific calculator to solve this. Thank you Click here to see answer by whty89(20)
 Question 26789: X to the power of 7 = 11.49 how do you solve for x Please provide with step by step instructions and also the use of scientific calculator to solve this. Thank you Click here to see answer by bmauger(101)

 Question 27041: How is Cramer's Rule done on both 2X2 and 3x3 Systems Click here to see answer by longjonsilver(2297)

 Question 27040: Hello my name is Charles and I have a question how do you fine the area of a triangle with vertices of (x1,y1),(x2,y2) and (x3,y3) I already know that the area = 1/2basexheight but it doesn't have equal sides Thank you for answering this question if you do Click here to see answer by longjonsilver(2297)
 Question 27040: Hello my name is Charles and I have a question how do you fine the area of a triangle with vertices of (x1,y1),(x2,y2) and (x3,y3) I already know that the area = 1/2basexheight but it doesn't have equal sides Thank you for answering this question if you do Click here to see answer by venugopalramana(3286)

 Question 27267: a theater contains 500 seats. For an upcoming talent show, the theater manager plans to sell \$4 and \$5 tickets. He must sell at least 200 \$4 tickets and 100 \$5 tickets for the show to be produced. He must bring in at least \$2000 to break even. How many tickets at each price should be sold to maximize income. I am asking this because the other time this is asked, there is no answer on it, just a statement that says It's already been answered. Click here to see answer by bmauger(101)

 Question 28309: Give examples of the following matrices: 2x2 identity matrix I2x2(the 2x2 is smaller then the I when written) 5x5 zero matrix 0 5x5 Two non zero matrices A and B such that AB=02x2 A 2x2 matrix C such that C does not = I2x2 but C 2(squared)=I2x2 Click here to see answer by longjonsilver(2297)

 Question 28312: Ok - I am having problems with solving the follwoing equation -- can you please help me out. Please note that the M amounts within the brackets are in sets of four -- 2 on top of 2 - for example M= a 0(being on the top line while 0 b are right below it -- lining up the a and the 0 and then the 0 and the b. Let M= [a 0] [0 b] with a, b real numbers. a) Solve that M(squared) =MM= [a(squared) 0] [0 b(squared)]. b) What is det(M)? c) Under what condition(s) does M(inverse) exist? d) What is M(inverse)? e) Suppose M= [2 0] [0 1]. What M(tenth power)? (hint: find M(squared), M(cube).... is there apattern? Click here to see answer by venugopalramana(3286)

 Question 28707: Please help!! Solve the following using matrices. x-3y+z=2 4x-12y+4z=8 -2x+6y-2z=-4 I am taking a class on-line and am not getting the one on one I need for these problems. thank you in advance Click here to see answer by longjonsilver(2297)

 Question 28603: I started this and then I could not get the answer to come out. Evaluate the determinant 5 2 3 5 2 4 2 3 2 Click here to see answer by longjonsilver(2297)

 Question 28600: I am having so much trouble with determinants. I have tried and tried but cannot figure these out. Evaluate the determinate 1/12 1/5 -5/9 5/7 Click here to see answer by longjonsilver(2297)

 Question 28602: Here's another one. I am not sure but I think that there may be no solutiuon to this. x -y + z = -3 x + y + z = 3 x + y -z = 7 Click here to see answer by longjonsilver(2297)