Posted: 3/19/2014 6:25:16 PM EDT
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Solve the system using inverse of matrix.
x+2y+3z= 6 x+y+z=10 2x+2y+ z= -1 this would be a 3x3 matrix correct? and it would be set up as 1 2 3 | 6 1 1 1 |10 2 2 1 | -1 ? |
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Seriously, the most general method for solving these kind of problems is not to compute the inverse, rather do Guassian Elimination with partial pivoting, reducing the matrix to upper triangular form and then do back-substitution to get the final solution. You could use the co-factor method to compute the inverse,but this is allot more work.
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and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. for everyone. is this a legit explination? http://www.youtube.com/watch?v=hu6B1d3vvqU |
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Quoted: never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. Quoted: Quoted: and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. |
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Linear algebra is a 300 level math course usually. It tends to be hard shit. The problem you are showing us is typical of the stuff you cover in the first few weeks of a linear algebra course. Quoted:
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and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. Some undergrad linear algebra classes begin with the definition of a vector space and never introduce calculations. 
OP: The matrix notation is used as a method to represent a system of 3 equations. The general idea is Ax=b so (A^-1)Ax = (A^-1)b => x = (A^-1)b |
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Some undergrad linear algebra classes begin with the definition of a vector space and never introduce calculations.
OP: The matrix notation is used as a method to represent a system of 3 equations. The general idea is Ax=b so (A^-1)Ax = (A^-1)b => x = (A^-1)b Quoted:
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and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. Some undergrad linear algebra classes begin with the definition of a vector space and never introduce calculations.
OP: The matrix notation is used as a method to represent a system of 3 equations. The general idea is Ax=b so (A^-1)Ax = (A^-1)b => x = (A^-1)b x=B? |
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x=B? Quoted:
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and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. Some undergrad linear algebra classes begin with the definition of a vector space and never introduce calculations.
OP: The matrix notation is used as a method to represent a system of 3 equations. The general idea is Ax=b so (A^-1)Ax = (A^-1)b => x = (A^-1)b x=B? Notation isn't the best here. Read here |
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Your textbook should have an example.
There are 2 common ways to find the inverse matrix of a 3x3 matrix: 1) Gauss-Jordan method = use row operations on [A|I] to turn it into [I|A] 2) determinant method Then X = (A^-1)B (Using a row operation on A is actually the same as multiplying A by a specific matrix... The product of all the row operation matrices needed to get A to I is... wait for it... A^-1) |
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never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. for everyone. is this a legit explination? http://www.youtube.com/watch?v=hu6B1d3vvqU Quoted:
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and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. for everyone. is this a legit explination? http://www.youtube.com/watch?v=hu6B1d3vvqU 7th grade algebra != college linear algebra |
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7th grade algebra != college linear algebra Quoted:
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and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. for everyone. is this a legit explination? http://www.youtube.com/watch?v=hu6B1d3vvqU 7th grade algebra != college linear algebra Yeah this is linear algebra. |
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Linear algebra is a 300 level math course usually. It tends to be hard shit. The problem you are showing us is typical of the stuff you cover in the first few weeks of a linear algebra course. Quoted:
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and this is more along the lines of linear algebra than pre-calc or calc never had this in Algebra. ever. I'm getting this in Pre Cal. content varies i guess in classes. The mechanics for manipulating simple small matrices used to be covered in high school, and other methods covered in freshmen science and engineering classes. The theory from rigorous linear algebra comes later. Here's a pretty good example of the process: http://www.mathcentre.ac.uk/resources/uploaded/sigma-matrices11-2009-1.pdf . I'd say reading the sheets leading up to this one would be a good idea. http://www.mathcentre.ac.uk/students/courses/mathematics/matrices/ |
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Matrix inverse takes forever. Just shove it into matlab or another calculator to shit out the answer. It's laborious to do matrix equations for large matrices, but later on, knowing how it is done makes the short cuts easier to understand, as well as the more advanced applications. I doubt they still teach the finite element method by hand, since most people have a computer, but I recall having to invert 10x10 matrices to find solutions for simple frames. Thank god Excel has a built in function for inverting matrices. |