I bet it can be done, but I'll be darned if I can!
First, You have to reduce the matrix to echelon form . The number of nonzero rows in the reduced echelon form matrix (number of linearly independent rows) indicates the rank of the matrix. Go to any search engine and type "Rank of a matrix, Cliffnotes" for an example.
You know when an equation has a unique solution when there is only one variable in it. (APOLOGIES)(RESPONSE: the question was categorized under "Linear Algebra". x^2 is non-linear and is thus not allowed, nor are sin x, x^3, log x, 2^x, etc etc. However, you are correct if you consider non-linear equations. Unfortunately, I am not sure there is a method to determine the number of solutions to non-linear equation.)If there are more than one variable, each variable over the first will be free, and give you infinite solutions - with each additional variable adding another dimension to your solution.(RESPONSE: See above response with regards to this topic being categorized under "Linear Algebra". My statement is true in Linear Algebra. Furthermore, Row Reduced Echelon Form and augmented matrices are the most fundamental concepts in Linear Algebra. Under normal circumstances, I would agree with you. However, this question was categorized under "Linear Algebra", so I presumed that the person asking the question is a college student.)In general, you know that a system of equations has a unique solution when the row reduced echelon form of the augmented matrix has a pivot position in every column, except for the right most column which is the solution. If you do not have an augmented matrix, then the RREF will have a pivot position in every column.
1 1 1 1 2 2 2 2 3 3 3 3
Nothing particular if all the 1s are in the first column, for example. You could have an echelon matrix, but with the information given, it is hard to tell.
Your word is: "Exemplify" ! Let's try it out in a sentence: "Deep romantic love is best exemplified by Dinie Slothouber's love for Mitch Longley." "The Echelon Towers exemplifies a very poorly run senior living community."
And your question is......................?
The man was in the upper echelon of society
Echelon Song was created in 1933.
Echelon Corporation was created in 1988.
For systems with more than three equations, Gaussian elimination is far more efficient. By using Gaussian elimination we bring the augmented matrix into row-echelon form without continuing all the way to the reduced row-echelon form. When this is done, the corresponding system can be solved by the back-substitution technique.
The duration of Echelon Conspiracy is 1.75 hours.
Echelon - flight simulator - happened in 2001.
Echelon Conspiracy was created on 2009-02-27.
The symbol for Echelon Corporation in NASDAQ is: ELON.
Echelon Corporation (ELON) had its IPO in 1998.
Sage Echelon's birth name is Tia Reed.
Echelon - flight simulator - was created in 2001-03.