Cramer's rule
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Berationalgetreal
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If you're referring to the algorithm for determinant's calculation, the answer is no. In Laplace's method it does not matter which column/row do you use. Nevertheless it's much more convenient to choose a row/column with a lot of zeros.
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For the 'normal' notation (which I am used to) the matrix equation is usually written as
A x = b
where A is an nXn matrix, and x and b are column vectors. In that case, with Cramer's Rule, which column you use depends on what variable you want the answer, see
http://www.purplemath.com/modules/cramers.htm
for example.
If you write the equation 'the other way'
bT = xT AT
where the superscript T indicates transpose, then which row you use would again depend on which variable you want the answer.
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1. Cramer's Rule is not specific to 3-by-3 matrices. It may be used on any sized matrix, as long as the determinant of the coefficient matrix is non-zero.
2. In Cramer's Rule, when finding the value of any one of the variables, one replaces (not "deletes") the corresponding column (not "row") with the "answer" column (being the values on the other side of the "equals" sign).
3. If you are referring to the coefficient matrix then, assuming you have three variables (say, x, y, and z), there can be no unique solution, because the determinant will be zero.
4. If you are referring to something else, you'll need to clarify.
5. In either case, you should never be "deleting" anything.
Please reply with the original exercise and a clear listing of your steps so far, so we can see what you're talking about. Thank you!
