what are 3 everyday uses for  matrices?
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Airline flight scheduling,. 2D & 3D graphics in Flash, Code-breaking
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Determining 3D protein structures in my line of work\n\nAlso used to determine the best ways to make alloys and composite materials
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definitely use MATLAB!
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There are many general properties of determinants of matrices for example\n\nConsider two matrices A and B then\ndet(AB)= det(A) det(B)\n\ndet(A) = det( Transpose(A) )\n\nIf you interchange two rows in a matrix then you will change the sign of the determinant.  Interchanging two columns does the same thing.\n\nThere are many more but these should get you started
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Use it as a serving tray,\nUse it as an exercising item,\nUse is for Candid Camera type situations,\nUse it for hiding credit cards,\nUse it for computing, internet, email, TV, DVD player, MP3 Player -if its working.
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If you're into the MATRIX look for a program called ZMatrix is wallpaper and a screen saver wrapped into one.  Really cool check it out!\n\nFor Xp uses check out Xp theams.
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Matrix algebra, a part of abstract algebra, is used to solve large system of equations. This is the basis for things various kinds of mathematical modeling programs such as economic forcasting, manufaturing production control, navigtation systems, etc.\n\nAnother areas where abstract algebra is used is in cryptography, i.e. generating encryption algorithms that protect your credit card number when you send it over the internet.\n\nWhat direct benefit you have from the knowledged will depend on what you plan to do with your future.
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You need math everyday. Shopping, paying bills, tipping, etc.
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At first I thought you were wanting the orthogonal matrices, but your example shows you are not. Orthogonal matrices are those whose inverse is their transpose. Yours are ones where the elements of the transpose are the inverse of the elements of the original.\n\nCertainly such a matrix has to have +-1 on the diagonal. Your matrix is singluar and any 2x2 matrix with your property and all 1 on the diagonal will be also. This means that one eigenvalue is 0 and the other is 2.\n\nI don't see anything special for 3x3 offhand, but I will look further.
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In general it used in negetive sense.\nFor example you are supposed to implement Matrix multiplication( or built a matrix object).\nThere is two way to show that your implementation works,\n1. create some matrix in your code and show with that. to test for another value you have to change the code.\n2. Take matrix as input from user.\n\nFirst practice is known as hardcore progrmming.
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Wow this question rocks because I found out that search engines like Yahoo and Google use this math trick to figure out which web sites are number one etc in page rank.\n\nIt is also cool for doing stretchy graphics manipulations in graphics programs and  video game designs.\n\nIn so-called "linear algebra" you can make a table or array of numbers (sort of like a spreadsheet) called a matrix. Hey, not "The Matrix" (bullet time rocks!), just "a" matrix.\n\nA matrix can be used for example to stretch, blur, focus, distort or otherwise transform an image. Some programs like PaintShop Pro even let you stuff numbers into a matrix to create a special-effects filter.\n\nIt is very useful to know the quantities called "eigenvectors" and "eigenvalues" for a matrix, because "eigen" is German for"Nuthing happening here dude". This means we can toss them away and make a complicated (big) matrix smaller. That's what "deflation" means. For computer programming you want fast, fast results so it helps to deflate big matrices BEFORE you start computing.\n\nThe Power method is a way to approximately find those pesky eigens using simple arithmetic. The math is not really too hard, you can manually do it with a $1 calculator, just multiplying and adding mostly. But it is best to use a computer program because it can be tedious.\n\nSo get out there and wipe out those eigens!!!
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This normally means that you are going to be using Gaussian (or Gauss-Jordan) reduction, where ther eare three "moves" that are allowed.\n\n1) You can switch any two rows in the matrix.\n2) You can multiply any row in the matrix by a non-zero scalar.\n3) You can add a multiple of one row to another.\n\nUsing these three "moves," the goal is to reduce the matrix into a usable form (the echelon form, for example).
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they are used on database file's and processors as shortcuts to things i aint got no example's but yea =)
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The only way you'll be able to get a solution to 3 linear equations with 2 unknowns is if there's a dependence relation on the rows or equivalently the columns.  Otherwise, there will be no solution.\n\nI haven't checked the determinant of your matrix but if there are no dependence relations on the rows or columns of the matrix that you gave, Gaussian Elimination will give you a single solution.  Alternatively, for small matrices like the one you have you can use Cramer's Rule more efficiently.\n\nEither way, your coefficient matrix seemes to represent 3 equations and 3 unknowns so I would proceed with Gaussian Elimination.
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sift\nfist\nfigs\ngist\nhist\nsigh
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you should use matlab.
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Math is used in music everywhere. A lot of the theory behind music deals with math. My theory professor in college was big into using math-like equations to solve theory problems. It can be used in the circle of fiths, finding intervals, chord progressions. About anything! A more recent math/music related thing is Schoenberg's 12 tone system. He uses math and notes to come up with all the different ways to arrange the 12 different notes on the keyboard. You can create a whole matrix just using a certain progression of notes. It's really interesting! To find more information try looking in some college music theory books. Or contact a theory professor at a local college! They could give you lots of good examples.