# 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 29835: I just dont understand this question. Let matrix A= 1 3 2 5 B= 2 3 1 2 C= 15 23 25 38 and suppose that AYB=C. Find the matrix Y. Thank you. Click here to see answer by kev82(148)

 Question 29838: I dont understand these Partician Matrices and how to break it up. Compute the following matrix 1 0 0 0 0 1 0 0 0 1 1 0 0 -1 0 1 The entire matrix is to the exponent 2006 Thank you so much! Click here to see answer by khwang(438)

 Question 30044: The value of square-root(2/pi) * Integral(e to the power -square(t)/2 ), where "t" is a variable from 4 to infinity is equal to what? Click here to see answer by venugopalramana(3286)

 Question 30193: Solve by using the Gaussian elimination method. For instance: 5x+2y=3 3x+4y=13 I seem to always get stuck on the fractions. Please help in details so I know how to solve more problems like this. Thank You. Click here to see answer by ikdeep(226)

 Question 30198: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work A square matrix is lower triangular if every entry above the diagonal is 0. a. Give an example of a 3x3 lower triangular matrix. b. Using your example from part (a), show that the determinant of a lower triangular matrix is the product of the entries on the diagonal. c. Show algebraically that the determinant of a 2x2 lower triangular matrix will always be the product of the entries on the diagonal. Click here to see answer by venugopalramana(3286)

 Question 30539: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work. Solve for the column vector v=[x] in the following matrix equation given that : [y] (Please note that the v has a curved arrow above it) A=[2 1] [1 -3] Av=[4] [-5] (please note that the v has a curved arrow above it) Click here to see answer by venugopalramana(3286)

 Question 30537: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work Let A and B be two 2x2 matrices. Show by example that the determinant function is multiplicative, that is, det(A)det(B) = det(AB) (here you can pick numeric examples for A and B). Bonus: show algebraically that the determinant function is multiplicative in the 2x2 case. Click here to see answer by mbarugel(146)

 Question 30324: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work. Solve for the column vector v =[x]in the following matrix equation given that: [y] For the problem above there is a little arrow above the v. A= [ 2 1 ] [1 -3] Av (there is a little arrow over the v)= [4] [-5] Click here to see answer by venugopalramana(3286)

 Question 30543: A company manufactures three styles of kitchen cabinets and each style comes in two grades. Style 1 requires 4 square units of plywood and 14 hours to build. Style2 requires 5 square units of plywood and 10 hours to build. Style 3 requires 3 square units of plywood and 8 hours to build. For grade A cabinets, the wood costs \$26 per square unit and labour costs \$35 per hour. For grade B, with cheaper material and less experienced cabinetmakers, the cost drops to \$20 per square unit and \$31 per hour. Display these figures in two matrices in such a way that their product shows the cost of materials and time required for each grade and style of cabinet. Calculate their product. Click here to see answer by mbarugel(146)

 Question 30595: Hi, Could someone please help be solve this problem. It is a maxtrix problem and I need to solve for x,y,and z using the Guss-Jordan Process. 3X-2Y+8Z=9 -2X+2Y+z=3 X+2y-3Z=8 Thank you so much!!!! Have a great day:) Sarah Click here to see answer by Fermat(127)

 Question 29946: I am so confused as to how to figured out a matrix problem using the Gauss-Jordan Method. Problem: 3X-2Y=-8Z+9 -2X+Z=-2Y+3 2Y-3Z+X=8 Thanks!!!! Click here to see answer by brianunlv(12)

 Question 31366: ) A brewery manufactures three types of beer - lite, regular, and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar and 1 bag of hops. Each vat of regular beer requires 4 bags of barley, 3 bag of sugar and 1 bag of hops. Each vat of dark beer requires 2 bags of barley, 2 bag of sugar and 4 bag of hops. Each day the brewery has 800 bags of barley, 600 bag of sugar and 300 bag of hops. The brewery realizes a profit of \$10 per vat of lite beer, \$20 per vat of regular beer, and \$30 per vat of dark beer. For this linear programming problem: (a) What are the decision variables? (b) What is the objective function? (c) What are the constraints? Click here to see answer by AnlytcPhil(1276)

 Question 31574: How do you to treat two equations in part (d)??? Two planes are defined by the equations given below. x + 3y + z = 1 (1) 2x + 7y − z = 1 (2) (a) Write down a normal to each of the planes. (b) How can you tell immediately that the planes are not parallel? (c) Write a quick test that shows they are not perpendicular. (d) Write the augmented matrix for the system of two equations, and find the solutions by row-reducing by hand. State clearly the row operations you use. (e) Hence find the line of intersection of the planes defined by the two equations. Give a direction vector for the line, and a point on the line. Why is it that text books only talk about three equations and to bad if you only have two??? What are the rules? Hours of time spent with no answers, It's madeness. Click here to see answer by venugopalramana(3286)

 Question 31557: (40) Use Cramers rule to solve for z: x+2y-3z=-24 2x-y+3z=13 x+2y+3z=0 POssible Answers: (A) -5 (B) -6 (C) -2 (D) 4 Thanks for your help Click here to see answer by mukhopadhyay(490)

 Question 31736: I have to put this in augmented matrix form, then I can solve. I need help finding variables. The average age of the Smith's cars is eight years. Three years ago the Toyota was twice as old as the Ford. Two years ago the sum of the Buick's and the Ford's ages was equal to the age of the Toyota. How old is each car now? x - toyota y - ford z - buick x + y + z/3 = 8 (..or x+y+z = 24 ?) in 2003 x = 2y (...or x - 3 = 2y -3 in 2004 y + z = z (...or (y+z)-2 = z - am I on the right track ???? thanks in advance Jane Click here to see answer by mbarugel(146)

 Question 32692: Use Cramer's Rule to solve the following pair of simultaneous linear equations: 3x = -7 + 2y; 5y = 8 - 2x Click here to see answer by mukhopadhyay(490)

 Question 32743: Find (a) hte discriminant, (b) the number of solutions and (c) the nature of the solutions for 5x^2-7x-4=0 Click here to see answer by mukhopadhyay(490)

 Question 32751: Find (a) the discriminant, (b) the number of solutions and (c) the nature of the solutions for 5x^2-7X-4=0 Click here to see answer by mukhopadhyay(490)

 Question 33426: How many solutions does a quadratic usually have? Find the missing value that makes the trinomial a perfect square x^2+20x+____ & x^2-3/4x+____ Click here to see answer by stanbon(57323)
 Question 33426: How many solutions does a quadratic usually have? Find the missing value that makes the trinomial a perfect square x^2+20x+____ & x^2-3/4x+____ Click here to see answer by sarah_adam(201)

 Question 33382: I need help with usings Cramer's Rule. The question is: Solve the following system of equations using Cramer's Rule. 2x + 4y - 3z = 2 2x - 2y + 3z = 3 3x - 4y + 5z = 4 I understand that I have to first have to set up the determinants. Which are D = 2 4 -3 Answer Column is 2 2 -2 3 3 3 -4 5 4 D of x = 2 4 -3 3 -2 3 4 -4 5 D of y = 2 2 -3 2 3 3 3 4 5 D of Z = 2 4 2 2 -2 3 3 -4 4 Now my problem is how do I evaluate the determinants? I think that I understand how to set it up. I'm just not sure what to do after that. Any help you can give me would be greatly appreciated. I'm not necessarily looking for the entire question, just an explanation of what to do next. I've looked over the web for hours and none of the Algebra websites explains how to do this step. Thanks for the help and have a great night. Jonna Click here to see answer by mukhopadhyay(490)
 Question 33382: I need help with usings Cramer's Rule. The question is: Solve the following system of equations using Cramer's Rule. 2x + 4y - 3z = 2 2x - 2y + 3z = 3 3x - 4y + 5z = 4 I understand that I have to first have to set up the determinants. Which are D = 2 4 -3 Answer Column is 2 2 -2 3 3 3 -4 5 4 D of x = 2 4 -3 3 -2 3 4 -4 5 D of y = 2 2 -3 2 3 3 3 4 5 D of Z = 2 4 2 2 -2 3 3 -4 4 Now my problem is how do I evaluate the determinants? I think that I understand how to set it up. I'm just not sure what to do after that. Any help you can give me would be greatly appreciated. I'm not necessarily looking for the entire question, just an explanation of what to do next. I've looked over the web for hours and none of the Algebra websites explains how to do this step. Thanks for the help and have a great night. Jonna Click here to see answer by venugopalramana(3286)

 Question 33389: I am completely stumped with this one! Please help! A company makes three products, A, B, and C. There are 500 pounds of raw material available. Each unit of product A requires 2 pounds of raw material, each unit of product B requires 2 pounds of raw material, and each unit of product C requires 3 pounds. The assembly line has 1,000 hours of operation available. Each unit of product A requires 4 hours, while each unit of products B and C requires 5 hours. The company realizes a profit of \$500 for each unit of product A, \$600 for each unit of product B, and \$1,000 for each unit of product C. Formulate (but don't solve) a linear program to determine how many units of each of the three products the company should make to maximize profits. Click here to see answer by mukhopadhyay(490)

 Question 30956: this uestion comes from a math 132 class the question is find the point of intersection the lines 2x+3y+6=0 and -2x+5y+10=0. If they do not intersect . state why they do not. I got 16/15 and 4/5 but i dont know doesnt look right. Thank you. Click here to see answer by venugopalramana(3286)

 Question 33611: evaluate the 3 x 3 determinant 3 4 -1 4 6 2 8 -2 3 Click here to see answer by Nate(3500)

 Question 33610: use the matrix approach to solve the system x+y-z= -3 2x+y+z= 4 5x-y+2z=23 I know this starts out with: 1 1 -1 | -3 2 1 1 | 4 5 -1 2 | 23 but I don't know what to do to each row to get the proper answers in the x, y, & z columns and the rows to be: 1 0 0 0 1 0 0 0 1 Click here to see answer by venugopalramana(3286)

 Question 33609: solve each system x+y-z= -1 4x-3y+2z= 16 2x-2y-3z=5 Click here to see answer by venugopalramana(3286)

 Question 33612: A box contains \$17.70 in nickels, dimes, and quarters. The number of dimes is 8 less than twice the number of nickels. The number of quarters is 2 more than the sum of the number of nickels and dimes. How many coins of each kind are there in the box? Click here to see answer by Paul(988)

 Question 33642: Please help me solve this problem (2x2 matrix) If A=[1 -2, 1 0] and AB=[1 0, -1 2]Find B. I tried multiplying A*AB changing the signs of AB but the answer did not come out right. Answer should be B=[-1 0, -1 1] Click here to see answer by Nate(3500)

 Question 31782: Use matrices to solve the following system. What is the value fo y? -4x-3z=7 x-2y-z=1 -5x+2y-z=1 POssible Soltuions: (A) -5 (B) -2 (C) 8 (D) 3 Click here to see answer by venugopalramana(3286)

 Question 33921: if the system below were written as a matrix equation, by which matrrix could you multiply both sides to obtain a solution? 4x + 6y = 24 5x = 8y = 40 Click here to see answer by fanism(39)

 Question 33915: i need help with matrices and systems of equations. [2 -1 1] [1 2 6] [3 -1 2] ____________ [2 -1 -2] [1 2 3] [3 -1 -1] represents the values of which variable in the solution of the equations below? 2x- y + z = -2 x +2y + 6z = 3 3x -y + 2z=-1 a) x b) y c) z d) none of the variables Click here to see answer by stanbon(57323)

 Question 33914: i need help with matrices and systems of equations. [1 -7 -1] [2 -3 2] [1 3 -2] ____________ [1 2 -1] [2 3 2] [1 -2 -2] represents the values of which variable in the solution of the equations below? x+ 2y - z = -7 2x +3y + 2z = -3 x-2y-2z=3 a) x b) y c) z d) none of the variables Click here to see answer by stanbon(57323)

 Question 34160: I have a problem getting the answers to these: Render the augmented matrix: 1 0 -1|2 0 2 1 |-1 1 0 1 |0 into row-echelon form and determine the value of the variables x,y and z. Also: 2.) Find the values of this matrix: 1 0 -1|0 0 1 0 |1 0 0 1 |2 Click here to see answer by venugopalramana(3286)

 Question 34228: Render the augmented matrix: 1 0 -1|2 0 2 1 |-1 1 0 1 |0 into row-echelon form and determine the value of the variables x,y and z. Also: 2.) Find the values of this matrix: 1 0 -1|0 0 1 0 |1 0 0 1 |2 Click here to see answer by kietra(57)

 Question 31744: Question: Use the matrices to solve the following system. What is the value of y? -4x-3z=7 x-2y-z=1 -5x+2y-z=1 Posbile Choices: (A) -5 (B) -2 (C) 8 (D) 3 Thank you for your help with this one! Click here to see answer by venugopalramana(3286)

 Question 31811: Can you help me with this question. Here is what it reads: Use matrices to solve the following system: What is the value of y? -4x-3z=7 x-2y-z=1 -5x+2y-z=1 Here are my possible choices: (a) -5 (b) -2 (c) 8 (d) 3 Thank you for your help Click here to see answer by venugopalramana(3286)

 Question 34768: Can you solve the following system of equations using Cramer's rule. 2x + 4y - 3z =2 2x - 2y + 3z =3 3x - 4y + 5z =4 Click here to see answer by AnlytcPhil(1276)

 Question 34772: Solve the following system of equations using Gaussian elimination (with a matrix) and back substitution, or by using Gauss-Jordan elimination. 3x + y - z = 0 x + y = 2z = 6 2x + 2y = 3z = 10 Click here to see answer by checkley71(8403)

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