# 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 168214: At the lake Curtis caught three fish .He wanted to wiegh the fish individually but his scale was broken -- it could only read weights between 5 and 10 pounds So he weighed the large and medium fish togethter and got 7.8 pounds The large and small fish weighed 7.0 pounds and the small medium fish were 5.6 pounds. How much did each fish weigh individually? What was the total weight of all three fish? Click here to see answer by stanbon(57347)

 Question 168333: use cramers rule to solve the system.. 3x+2y=-2 5x+4y=8 Click here to see answer by Juhi(44)

 Question 168678: As a receptionist for a veterinarian, Sue schedules appointments. She allots 20 minutes for a routine office visit and 40 minutes for a surgery. The vet cannot do more than 6 surgeries per day. The office has 7 hours available for appointments. If the office visits cost \$55 and most surgeries cost \$125, how many office visits and surgeries should Sue schedule to maximize the veterinarian's profit/ I am not sure how to set up the constratints and graph. Click here to see answer by ankor@dixie-net.com(15652)

 Question 168727: solve the systme by using an augmented matrix 4x+y-z=7 -2x+2y+5z=3 7x-3y-9z=-4 Click here to see answer by Alan3354(30993)

 Question 168729: Suppose you want to use Cramer's rule to find the value of z in the following system.. write the determinants you would need to evaluate. Click here to see answer by Edwin McCravy(8909)

 Question 168726: Solve the system by using an augmented matrix. Click here to see answer by Edwin McCravy(8909)

 Question 169287: I need to find the inverse of the matrix [ -6 15 ] I tried but it doesn't look right. [ 5 -8 ] Click here to see answer by Fombitz(13828)

 Question 170125: How do i solve this in matrix form: 2x+8y=22 4x+ y=14 Click here to see answer by jim_thompson5910(28595)

 Question 170126: 3. A companys employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 22 carbohydrates and 14 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work to receive full credit. Carbohydrates Protein Peanut Butter 2 4 Oats 8 1 A. Write an equation for the total amount of carbohydrates. B. Write an equation for the total amount of protein. C. Determine the augmented matrix that represents the previous two equations. D. Solve for the previous matrix. Show all work to receive full credit. E. How many tablespoons of each will there need to be for the new energy bar? 4. A total of 700 tickets were sold for a musical. Senior citizen tickets sold for \$15, children tickets sold for \$20, and adult tickets sold for \$25; the total earnings from ticket sales was \$15,750. Five times more children tickets were sold than senior citizen tickets. How many tickets of each type were sold? Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit. A. What are the three unknowns? B. Write a separate equation representing each of the first three sentences of the word problem. C. Determine the augmented matrix that represents the three equations. D. Solve for the matrix. Show all work to receive full credit. E. How many of each type of ticket were sold? Click here to see answer by stanbon(57347)

 Question 170362: Find X, Y, and Z. 5x + 4y - 2z = 3 4x - 2y + 5z = -16 2x + 5y + 4z = -5 Click here to see answer by Edwin McCravy(8909)

 Question 171320: let A be a 5 X 3 matrix and B be a 3 X 5 matrix a) is it possible to add A and B?..yes it is possible to add A and B b) is it possible to do the mulitplication AB c) is it possible to do the mulitpilcation BA?...of course is it possible to multiply A and B Click here to see answer by Edwin McCravy(8909)
 Question 171320: let A be a 5 X 3 matrix and B be a 3 X 5 matrix a) is it possible to add A and B?..yes it is possible to add A and B b) is it possible to do the mulitplication AB c) is it possible to do the mulitpilcation BA?...of course is it possible to multiply A and B Click here to see answer by slasha(1)

 Question 171695: I don't understand the steps of the Matrix for these equations. Could you please show me? 7x+8y-z=9 x-2y-5z=-31 -7x+y+z=0 Your help is highly appreciated! Thank you so much! Click here to see answer by Edwin McCravy(8909)

 Question 172106: Could you please show me how to do matrix for these equations? I don't understand how it works. 7x+8y-z=9 x-2y-5z=-31 -7x+y+z=0 Thank you so very much for your time and help! I really appreciate it! Click here to see answer by Alan3354(30993)

 Question 172378: calculate the determinant |1 3 0| |0 -3 4| |2 5 -1| Click here to see answer by Alan3354(30993)

 Question 173298: write the following in matrix equation form. solve the following system of equations. 5x+5y=50 0.05x+0.14y=5000 Click here to see answer by Alan3354(30993)

 Question 173296: A financial manager wants to invest \$23000 for a client by putting some of the money in a low-risk inverstment that earns 7% per year and some of the money in a high risk investment that earns 10% per year. create an appropriate matrix to solve the given situation. how much money should be invested at each intrest rate to earn \$5000 in intrest per year? Click here to see answer by Mathtut(3670)
 Question 173296: A financial manager wants to invest \$23000 for a client by putting some of the money in a low-risk inverstment that earns 7% per year and some of the money in a high risk investment that earns 10% per year. create an appropriate matrix to solve the given situation. how much money should be invested at each intrest rate to earn \$5000 in intrest per year? Click here to see answer by checkley77(12569)

 Question 173732: Solve the system of equations using matrices (row operations). -4x-6y-z=-25 x-4y+3z=9 -7x+y+z=-7 Click here to see answer by Edwin McCravy(8909)

 Question 172008: find the inverse of matrix. 1. 2. 3. Click here to see answer by Edwin McCravy(8909)

 Question 173944: at a local farmers market,Jane sold 27 squash,31 tomatoes,24 peppers,and 18 melons.Jose sold 48 squash,72 tomatoes,61 peppers, and 25 melons. a)Create a 2x4 matrix of this data.Name this matrix P. b)What is the address of the number of peppers that jane sold? c)What is the address of the data stored in the second row and first column?What does this entry represent? d)Could you have created a matrix with different dimensions from the created part a? Click here to see answer by Edwin McCravy(8909)

 Question 174121: please give me the answers.. use a caret (^) to indicate the power. For example, 53 would be written as 5^3. 1. Write the equation of a polynomial that has zeros at 3 and 2. Write each polynomial function in standard form. Then classify it by degree and by the number of terms. 2. n = 4m2  m + 7m4 n = 4m3 + 4m  2; cubic trinomial n = 7m4 + 4m2  m; quartic trinomial n = 4m4 + 8m2  m ; quartic trinomial n = 3m3 + 2m  5; cubic trinomial 3. f(t) = 4t + 3t3 + 2t  7 f(t) = 3t3 + 6t  7; cubic trinomial f(t) = 2t3 + 4t  1; cubic trinomial f(t) = 5t3 + 2t  7; cubic trinomial f(t) = 7t3 + 3t  4; cubic trinomial 4. f(r) = 5r + 7 + 2r2 f(r) = 8r3 + 5r + 1; cubic trinomial f(r) = r2 + 5r + 7; quadratic trinomial f(r) = 2r3 + 5r + 7; cubic trinomial f(r) = 2r2 + 5r + 7; quadratic trinomial For each function, determine the zeros and their multiplicity. 5. y = (x + 2)2(x  5)4 2, multiplicity 2; 5, multiplicity 4 2, multiplicity 2; 5, multiplicity 3 2, multiplicity 4; 5, multiplicity 2 2, multiplicity 2; 7, multiplicity 4 6. y = (3x + 2)3(x  5)5 4, multiplicity 2; 5, multiplicity 2 3, multiplicity 4; 2, multiplicity 4 , multiplicity 3; 5, multiplicity 5 2, multiplicity 3; 5, multiplicity 5 7. y = x2(x + 4)3(x  1) 2, multiplicity 2; 4, multiplicity 2; 1, multiplicity 1 0, multiplicity 2; 4, multiplicity 3; 1, multiplicity 1 3, multiplicity 4; 3, multiplicity 2; 2, multiplicity 3 0, multiplicity 2; 3, multiplicity 2; 2, multiplicity 3 8. (x3 + 3x2  x  3) χ (x  1) 10. Use synthetic division to find P(3) for P(x) = 2x4  3x3  x + 4. Click here to see answer by stanbon(57347)

 Question 174388: Find the inverse of each matrix, if it exists... 1.. [-2 -1] [10 7] 2..[-4 2] [-5 1] 3.. [9 -3] [-6 2] 4.. [3 4] [6] [2 3] x=[5] 5..[1 -6 0] [1] [0 1 -7]x=[4] [3 0 2] [11] Click here to see answer by Mathtut(3670)

 Question 173807: Find matrix X: AX= B 1. A= [6,5] B= [18,49] [4,-2] [-20,6] 2. A= [3,4] B= [10,-10] [-3,-2] [-8,8] Click here to see answer by Mathtut(3670)

 Question 174120: Find the inverse of each matrix, if it exists. 1.[ -2 -1] [10 7] 2.[-4 2] [-5 1] 3.[9 -3] [-6 2] 4. [3 4] [2 3] x=[6/5] 5. [2 -3] x+[-1 7] [9 12] [1 2] [-2 4]=[3 10] 6.. [1 -6 0] [0 1 -7] x=[1] [3 0 2] [4] [11] Click here to see answer by Mathtut(3670)

 Question 174415: ``` what is the value of this determinant? thank you!``` Click here to see answer by Edwin McCravy(8909)

 Question 174521: Hi. I'm having a lot of trouble with this question. Suppose you invested \$5000 in three different funds for one year. The funds paid simple interest of 8%, 10%, and 7%, respectively. The total interest at the end of one year was \$405. You invested \$500 more at 10% than at 8%. How much did you invest in the 10% fund? The answer of the book is \$1500, but I really need to know how to get there and I would really appreciate it your help. THANKS! Click here to see answer by Earlsdon(6287)

 Question 174529: Hi. I have tried solving this, but I am not sure if it's right and would really appreciate your help. A hardware store mixes paints in a ratio of two parts red to six parts yellow to make pumpkin orange. A ratio of five parts red to three parts yellow makes red-pepper red. A gallon of pumpkin orange sells for \$25, and a gallon of red-pepper red sells for \$28. A. Write a system of equations to model the situation (for this one i wrote 2r+6y=25 and 5r+3y=28, but I dont know if it is correct) B. Solve the system (I got r=31/8 and y=23/8) C. Find the cost of 1qt of red paint and the cost of 1qt of yellow paint. Ok, this one I don't know. I would really appreciate your help. THANKS! Click here to see answer by josmiceli(9678)

 Question 174531: While stranded on an island, the crew of a sailboat has access to only three sources of food, as shown in the table below. One of the crew members designs a daily diet to supply each person with 120g of fat, 220g of carbohydrates, and 80g of protein. _______________ A______B_______C Fat____________ 10 g____ 4g_____ 12 g Carbohydrates___11 g___77 g_____0g Protein_________4 g_____1 g_____16 g A. Write a system of three equations in three variables to find the number of portions of each food each person must have to meet the daily diet. B. Use an augmented matrix to solve the system of equations from part (a). C. Suppose food C runs out. How would this change the number of portions of food required each day? Click here to see answer by Mathtut(3670)

 Question 174551: As a participant in your school's community service project, you volunteer a total of 40 hours over the course of the school year. Your volunteer hours include serving at a soup kitchen, picking up trash at several local parks, and collecting toys for needy children. You spend 4 times as many hours collecting toys as picking up trash, and 2 hours less serving at the soup kitchen than picking up trash. 1. Solve this system of equations using Cramer's Rule. Click here to see answer by Mathtut(3670)

 Question 174668: As a participant in your school's community service project, you volunteer a total of 40 hours over the course of the school year. Your volunteer hours include serving at a soup kitchen, picking up trash at several local parks, and collecting toys for needy children. You spend 4 times as many hours collecting toys as picking up trash, and 2 hours less serving at the soup kitchen than picking up trash. Slove this system of equations using Cramer's Rule. Suppose you cannot remember the total number of hours you volunteered. From the remaining information, can you still determine how many hours you spend doing each volunteer activity? Why or why not? Click here to see answer by Mathtut(3670)

 Question 174673: In this problem, they give me the diagram of a rectangle with a diagonal dividing it in two triangles. Each corner is labeled with A, B, C, and D. The perimeter of a rectangle is 28 cm. The perimeter of each of the triangles is 24 cm. The diagonal of the rectangle is 2 cm longer than the longer side of the rectangle. How do you write a system of three questions in three unknowns? How do you simplify the system to a system of two equations in two unknowns? And how can I write an augmented matrix for the system? This is what I've done so far: 2a+2b=28 a+b+x=24 2+a=? Thankyou&Happy New Year!! Click here to see answer by Mathtut(3670)
 Question 174673: In this problem, they give me the diagram of a rectangle with a diagonal dividing it in two triangles. Each corner is labeled with A, B, C, and D. The perimeter of a rectangle is 28 cm. The perimeter of each of the triangles is 24 cm. The diagonal of the rectangle is 2 cm longer than the longer side of the rectangle. How do you write a system of three questions in three unknowns? How do you simplify the system to a system of two equations in two unknowns? And how can I write an augmented matrix for the system? This is what I've done so far: 2a+2b=28 a+b+x=24 2+a=? Thankyou&Happy New Year!! Click here to see answer by stanbon(57347)

 Question 174705: [6-a 4] * [-2] = [2a] [-3 -3(d-2] * [3] = [-3] find a and d... this is a matrice Click here to see answer by stanbon(57347)

 Question 174862: I have to determine the number of each type of seats in a 2400 seat stadium and solve the equation: n= number of nosebleed seats; g=number of general admission seats and p= number of press box seats. Click here to see answer by Mathtut(3670)

 Question 174917: i have the following 3x3 matrix 1,2,-1 2,1,4 = A 1,-2,1 i need to evaluate A^2 and A^3 but i cant even figure out where to start, any help would be greatly appreciated Click here to see answer by actuary(112)

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