Critical Thinking-Logical Proo

Want to read the rest of this paper? Join Essayworld today to view this entire essay and over 50,000 other term papers

the permutation of the elementary products is odd (Hughes-Hallet 20). These two numbers are then multiplied by their respective permutation and the whole lot is added together. When all calculations are said and done this results in a number for matrix A, in this case -58. This now leads us to the definition of an eigenvalue. Since we have already defined A as a n x n matrix we can say that the eigenvalues are the solutions of the equation obtained from taking the determinant of the matrix A subtracted from the product of the identity matrix and the variable lambda (Hughes-Hallet 90). The identity matrix is defined as a matrix with ones along it's diagonal and zeros everywhere else (Yaquib 23). Now having a rough idea of what the determinant and eigenvalues are we can proceed with discussion of the argument.
Is this a valid argument? The definition of validity explains in order to be valid the argument must have the characteristic that it's conclusion absolutely follows from the ...

Get instant access to over 50,000 essays. Write better papers. Get better grades. Already a member? Login

within this space. We can then let one subspace be defined as the n x n matrices that have a determinant while the other subspace will be defined as product of the eigenvalues of the n x n matrices. We know from the definition of determinant and the definition of eigenvalue that it is logically possible for them to be equal since there is no stipulation that prevents this from happening. Therefore it is logically possible for the determinant of an n x n matrix to equal the product eigenvalues of an n x n matrix. This means that the argument is valid, however this does not show soundness.
In order to prove whether or not this argument is sound, several assumptions have to be made. The ...

Succeed in your coursework without stepping into a library. Get access to a growing library of notes, book reports, and research papers in 2 minutes or less.

CITE THIS PAGE: