Learn how systems of linear equations can be represented by augmented matrices.
Log in ana k 8 years agoPosted 8 years ago. Direct link to ana k's post “Is there a reason the ver...” Is there a reason the vertical line representing = is not used in this instance? • (73 votes) Coen francis 7 years agoPosted 7 years ago. Direct link to Coen francis's post “Although I personally agr...” Although I personally agree that it is very useful. (1 vote) Gigi Greene 8 years agoPosted 8 years ago. Direct link to Gigi Greene's post “Why does the + sign turn ...” Why does the + sign turn into - when put into standard form? • (15 votes) Shreya 8 years agoPosted 8 years ago. Direct link to Shreya's post “Say you have the equation...” Say you have the equation 3x+2y+8=0. (70 votes) Amn Ashhad 6 years agoPosted 6 years ago. Direct link to Amn Ashhad's post “Do the matrix have to be ...” Do the matrix have to be in alphabetical order? • (7 votes) Ian 6 years agoPosted 6 years ago. Direct link to Ian's post “When Sal writes letters i...” When Sal writes letters in the matrices, they are just variables; they can be anything they want. So, no, they don't have to be in alphabetical order. It just makes it more simple to see and read. (15 votes) Tiffanie L. 7 years agoPosted 7 years ago. Direct link to Tiffanie L.'s post “Why are system of equatio...” Why are system of equations represented in matrix format if it's harder to simplify? How do you solve a matrix system of equations? • (5 votes) kubleeka 7 years agoPosted 7 years ago. Direct link to kubleeka's post “There are things called m...” There are things called matrix row operations that let you rearrange the entries of a matrix while leaving the underlying system of equations "the same". Each row operation corresponds to a valid operation on the system of equations, like adding two equations together, writing them in a different order, or multiplying by a constant. You can perform these matrix operations in a rote, mechanical way to find the solution set to any system of equations (if one exists). The goal of representing systems of equations like this is to remove the creative element from solving systems and provide an algorithm for solving them. (7 votes) talal.waseem3 6 years agoPosted 6 years ago. Direct link to talal.waseem3's post “So when there is a variab...” So when there is a variable in one of the equations but not in the other the number 0 is like a placeholder correct? • (6 votes) Sahil Madisetti 4 years agoPosted 4 years ago. Direct link to Sahil Madisetti's post “that's correct yeah the p...” that's correct yeah the placeholder of the other equation when the variable is not there (1 vote) coolaa 3 years agoPosted 3 years ago. Direct link to coolaa's post “What exactly would a 2x2 ...” What exactly would a 2x2 matrix represent? Would column 1 represent x and column 2 represent a constant x is = to? Would this simply represent 2 equations defining x? • (2 votes) KLaudano 3 years agoPosted 3 years ago. Direct link to KLaudano's post “Typically, each row in a ...” Typically, each row in a matrix represents an equation and each column represents a variable. A 2x2 matrix could be used to represent two linear equations. For example, we could put y = 3x + 5 and y = -x + 2 into the following matrix. | 3 5 | (3 votes) Gabrieliz A. Ramirez Martinez a year agoPosted a year ago. Direct link to Gabrieliz A. Ramirez Martinez's post “the last one dont make an...” the last one dont make any sense • (2 votes) Manny a year agoPosted a year ago. Direct link to Manny's post “If you mean the last ques...” If you mean the last question from challenge problems, it formatted in a way to kinda trick you. (4 votes) mukukacaiphasbwalya 4 years agoPosted 4 years ago. Direct link to mukukacaiphasbwalya's post “How to find a determinant...” How to find a determinant and an inverse of a given matrix • (3 votes) Voldigoat27 9 months agoPosted 9 months ago. Direct link to Voldigoat27's post “The inverse of a matrix e...” The inverse of a matrix exists if and only if the determinant is nonzero. To find the inverse of a matrix, we write a new extended matrix with the identity on the right. Then we completely row reduce, the resulting matrix on the right will be the inverse matrix (1 vote) Can we represent the augmented matrix of a set of equations with the variables jumbled up in any manner if the equations consist of (x,y,z) and constants • (2 votes) Justin Woodward 8 years agoPosted 8 years ago. Direct link to Justin Woodward's post “the equation itself can b...” the equation itself can be jumbled up and has been in the final example on the page. However when putting it back into a matrix it needs to be x,y,z then the answer. in their respective rows. (2 votes) Domenick Mitchell 6 years agoPosted 6 years ago. Direct link to Domenick Mitchell's post “Why do numbers 5 and 6 ha...” Why do numbers 5 and 6 have asterisks in the question? There isn't any little footnote or footer or whatever you want to call it there. Here is #5 as follows, 5*) Which system is represented by the augmented matrix?, and also #6 as follows, 6*) Which matrix represents the system? • (2 votes) Evan Lewis 6 years agoPosted 6 years ago. Direct link to Evan Lewis's post “Those are the Challenge p...” Those are the Challenge problems, so I believe the asterisks are used to indicate they are harder problems. (2 votes)Want to join the conversation?
Then to get this equation in the standard form you will subtract both sides of the equation by 8. And you'll get 3x+2y=-8. So that's how you get the negative sign.
But that doesn't happen always. If you have 3x+2y-8=0, then you'll get 3x+2y=8.
Hope that helps. :)
|-1 2 |
3x+2=12y, which is not in the standard form. We can rewrite it as 3x-12y=-2. The second one is -8y= 2x+15, which is also not in standard form. Rewriting it we get 2x+8y=-15. Now if we write express this as a matrix, we get
[3 -12 -2 ]
[2 8 -15]
But there is no such option. So, lets revisit an equation and modify it so that it would match with one in the options. Take 2x+8y=-15 . Multiplying both sides by -1, we get -2x-8y=15. Now, we get
[ 3 -12 -2 ]
[-2 -8 15]
(Note: I didn't take the first equation since all the options have 3 in its first column, first row).
This is option C. Hence it is the answer.
eg. 4x + 6y - 5z = 12
12x - 3y + 4z = 5
can we represent the augmented matrix as the following;
[4 -5 6 12]
[12 4 -3 5]
switching the (y) with (z) or should it be in the same order as it is given in the equation/ the alphabetical order??
