# 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 34777: I am having a really hard time understanding the Gauss-Jordan Method. I have reviewed everything I could possibly find on this subject and it seems like there is no formal way to do this. I need a method to the madness? Please help if you can... Use the Gauss-Jordan Mathod to solve these systems of linear equations. Problem #1: x+y+z=5 y+z=1 2z=4 Problem #2: x+y=1 2x+3y=0 Your explanations of how to understand this method is greatly appreciated. Thanks! Click here to see answer by checkley71(8403)

 Question 34779: Find the inverse of the following matrix. A = [2 4] [1 -3] Click here to see answer by venugopalramana(3286)

 Question 35030: Solve the following variable using Cramer's Rule. Reduce fraction, if possible. -9x + 1y + 6z = -7 5x + 4y - 5z = -1 2x -8y - 2z = 8 Click here to see answer by longjonsilver(2297)

 Question 35190: The augmented matrices for three separate systems of linear equations in the variables x, y, z, and w, respectively, have been reduced to the row echelon forms given below. Find the solutions to each of the systems. A = 1 0 1 −1 : 3 0 1 3 1 : −1 0 0 1 1 : 2 0 0 0 0 : 1 , B = 1 0 0 1 : 3 0 1 0 −2 : 1 0 0 1 3 : −3 0 0 0 0 : 0 , C = 1 1 2 −2 : 0 0 1 −3 1 : 4 0 0 0 1 : 3 So with respect to A and row four where 0=1 does that mean that this system can not be solved or can it? What is the rule here? Click here to see answer by stanbon(57337)

 Question 35197: Use Gaussian Elimination to reduce the augmented matrix for the following system of linear equations to upper triangular form, and use back-substitution to solve the system. x + y − z = 3; (1) −x + 2y + z = 0; (2) 2x − y − z = 1. (3) The book gives the answer but not how to get the answer. Please i need to understand what they mean. Click here to see answer by stanbon(57337)

 Question 35199: Show that AB = BA is not true in general for matrix multiplication, by offering a coun-terexample with matrices A and B of the same size. Give your own matrices. So is the following in example I used A=|2,4|and B=|2| .....|4| |2,4|*|2| .........|4| is not = to |2|*|2,4| |4| have I got it right? Click here to see answer by stanbon(57337)

 Question 35276: factor the matrix A into a product of elementary matrices. A= [1 1] [2 1] Click here to see answer by venugopalramana(3286)

 Question 33970: (1)A=[-3 2] B= [0 2] (find AB and BA if possible) [2 -2] [-2 4] (2)A=[-2 3] B=[ 3 ] (find AB if possible) [1 -2] [-2 ] [0 0] (3)A=[2 -2 4] B=[2 1 -3 0] [1 0 -1] [0 -2 1 -2] (find AB if possible) [2 1 3] [1 -1 0 2] I am having trouble with these problems i hope you can help me thank you Brittny Click here to see answer by venugopalramana(3286)

 Question 36265: using cramer's rule, how would you solve for a 4 by 4 matrix? i.e.- 4x + 0y + 3z - 2w = 2 3x + y + 2z - w = 4 x - 6y - 2z + 2w = 0 2x + 2y + 0z - w = 1 Click here to see answer by stanbon(57337)

 Question 36582: Solve the determinant 3 x 1 1 = 2 (the 3 x and 1 1 are inside determinant signs) Click here to see answer by venugopalramana(3286)

 Question 37509: Find det A, given A = [-1 0 1 2-1 3 0 1 5] Click here to see answer by fractalier(2101)

 Question 39275: Use Cramer's Rule to solve for z: 3x+2y-z=17 2x+3y-z=15 2x-3y-z=-3 Click here to see answer by longjonsilver(2297)

 Question 39277: And last one for the day... Evaluate: 4 -1 3 5 2 -4 3 -5 2 Click here to see answer by stanbon(57337)
 Question 39277: And last one for the day... Evaluate: 4 -1 3 5 2 -4 3 -5 2 Click here to see answer by checkley71(8403)

 Question 39274: Find the values of A and B in the following partial fraction decomposition. 11x-2/x^2+x-6= A/x+3+B/x-2 Click here to see answer by fractalier(2101)

 Question 39401: Please help this is a multiple choice, but I believe there are several answers, For the rational expression 6x^2+9x-2/(x-3)^2(x+5) choose all of the terms below that are included in its partial fraction decomposition. The choices are a) A/x^2+2x-15 b)A/x+5 c)B/x-3 d)C(x-3)^2 Thanks Click here to see answer by fractalier(2101)

 Question 39449: Use Cramer's Rule to solve this equation. 2x-5y=18 -x+3y=10 Click here to see answer by longjonsilver(2297)

 Question 39448: Use Cramer's Rule to solve this equation. 7x-2y=4 3x+y=-6 Click here to see answer by longjonsilver(2297)

 Question 39491: Use cramers Rule to solve the Linear system {5x-4y=8 {2x+7y=-3 solve the equation 5x2-8=22 solve the equation 3x2+5x2-1=0 Click here to see answer by checkley71(8403)

 Question 39759: Gauss Jordan...Please Help A system of three linear equations in the variables x,y and z is represented by an augemented matrix. The first two rows of this augmented matrix are shown. Using the Gauss Jordan method to solve the system, the next step is to make the entry in row 2, column 1 equal to zero by multipling row 1 by a constant and adding that result to row two. Now I am stuck I keep not getting the right answer to complete row two of the new augmented matrix... 1 3 4 2 I have...1 3 4 2 4 5 7 9 0 .. .. .. Click here to see answer by fractalier(2101)

 Question 40076: please help me with this problem. what is the value of the determinant. [3 6 8] [2 4 0]? [3 6 8] (this is one determinant) Click here to see answer by stanbon(57337)

 Question 40075: please help me with this problem. solve the following equation [0 0 -1] [3 x 0 ] =x2 (x2 is x square and the equation is one matrix) [2 0 3] Click here to see answer by stanbon(57337)

 Question 40783: use cramers rule to solve 5x-4y+z=17 x+y+z=4 -10x+8y-2z=11 Click here to see answer by venugopalramana(3286)

 Question 40782: Use cramers rule to solve 2x+3y+z=0 5x+y-2z=9 10x-5y+3z=4 Click here to see answer by venugopalramana(3286)

 Question 40781: Use Cramers rule to solve the equation 4x+8y=12 3x+6y=9 Click here to see answer by venugopalramana(3286)

 Question 40780: Use Cramers Rule to solve the system of linear equation 3x+5y=17 x+3y=15 Click here to see answer by venugopalramana(3286)

 Question 41095: Evaluate the deteminant 1 0 -1 -2 3 5 6 -3 4 Click here to see answer by fractalier(2101)

 Question 41173: solve the following system of equations. x-2y=5 -3x+2y=7 Click here to see answer by PaulAllen65270(19)

 Question 41176: use the Gauss-Jordan elimination to solve the following system of equations. x+y+z=2 2x-3y+z=-11 -x+2y-z=8 Click here to see answer by zeynep(43)

 Question 41177: use Gauss-Jordan elimination to solve the following system of equations. 3x+5y=7 6x-y=-8 Click here to see answer by zeynep(43)

 Question 41880: In the algebra of matrices why does there have to be a right and left distributive property? Click here to see answer by venugopalramana(3286)

 Question 42078: Could you please solve this for me using cramer's rule...I have tried 3 times and I keep getting different answers, and none of them are the given answers. -x-4y-z=-3 -2x+2y-6z=-3 -x-4y-z=-3 She said that the first and the third equation are a hint...I'm confused please help! Click here to see answer by psbhowmick(529)

 Question 42432: Find the determinant of the matrix 5 2 -6 3 Click here to see answer by rapaljer(4667)

 Question 42586: A single dose of a dietary supplement contains 0.2 gram of calcium and 0.2 gram of vitamin C. A single dose of a secondary supplement contains 0.1 gram of calcium and 0.4 gram of vitamin C. If a person wants to take 0.6 gram of calcium and 1.2 grams of vitamin C, how many doses of each supplement should she take? I'm guessing you have to write a system of equations but I'm not sure how it should be. This is my guess: (a= calcium, c= vitamin C) 0.2a + 0.2c = ? 0.1a + 0.4c = ? I don't know if that's anywhere near correct but if it is, I have no clue what the equations should equal to. Please help! Thank you. Click here to see answer by Nate(3500)

 Question 43320: Help with this matrix would be much appreciated! find and write the linear system corresponding to matrix and solve it [1 0 0 | 7 ] [0 1 0 | -3 ] [0 0 2 | 6 ] Click here to see answer by fractalier(2101)
 Question 43320: Help with this matrix would be much appreciated! find and write the linear system corresponding to matrix and solve it [1 0 0 | 7 ] [0 1 0 | -3 ] [0 0 2 | 6 ] Click here to see answer by psbhowmick(529)

 Question 43340: Solve the matrix equation: |4-5||m|=|32| |1 2||n |=|-5| Thank You Click here to see answer by venugopalramana(3286)

 Question 43319: Please help with this one... perform the indicated row operation on the matrix [-1 3 | 2] [2 0 | 4] operation: 2Rsubscript1, +Rsubscript2, ->Rsubscript2 Click here to see answer by venugopalramana(3286)

 Question 44037: Write the augmented matrix for each system of equations x + 3y = 5 y - 4z = 8 -2x = 5z = 7 Click here to see answer by venugopalramana(3286)

 Question 44235: Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent x + 2y = 3 2x + y = 5 Click here to see answer by AnlytcPhil(1276)

 Question 44237: Solve each system by substitution. Determine whether each system is independent, inconsistent, or dependent 2y = 1 - 4x 2x + y = 0 Click here to see answer by AnlytcPhil(1276)

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