What professions use Linear Algebra's System of Equations and how are they used?
81619
Mail carriers use linear algebra as you and I use linear algegra. Stamp buyers use linear algebra. Anyone who counts money at home or at a profession uses linear algebra.\n\nFor postage of $1.62, how many 1$ stamps, $.50 stamps, $.39 stamps, etc to equal $1.62. \n\nWe use:\n\n $1 (x) + $.50 (y) + $.39 (z) + $.01 (w) = $1.62\n\nwhere x is number of dollar stamps, y is number of fifty cents stamps, z is number 39 cents stamps, and w is number of 1 cent stamps. \n\nWhat happens if mail carrier at counter says I don't have fifty cent stamps but I do have ten cents stamps. Then another linear equation is introduced that equals $1.62.
236017
sorry i don't know mathematica but you can solve it easily using matlab. Enter rthe coefficient matrix as follows for example,\nA=[1 2 3 4; 2 3 3 4;........]\nand the right hand side\nb=[ 2 3 4 4]\nonly for illustration. ";"indicates columns.\nA/b solves this system and gives the solution vector x.
634747
What you want is express \n\nv = a*v1 + b*v2 + c*v3 \n\nWhere a, b and c are, of course, scalars. The coordinate vector will then be (a, b, c).\n\nNow how do we do this: \n\n(2, -1, 3) = a(1, 0, 0) + b(2, 2, 0) + c(3, 3, 3) \n\nEither you just look at it and try to guess what a b and c can be, or you write this up as a set of 3 equations in a,b and c: \n\n2 = 1a + 2b + 3c\n-1 = 0a + 2b + 3c\n3 = -0a + 0b + 3c \n\n...and then solve it: \n\nFrom the last equation we see that c = 1, then using the second equation, -1 = 2b + 3  <=>    -4 = 2b  <=>  -2 = b\n\nAnd substituting into the first, \n\n2 = 1a + 2(-2) + 3(1) = a - 4 + 3 = a - 1 \n\nthus 3 = a. \n\nSo the coordinate vector is (3, -2, 1) and with these numbers the criteria are (supposedly) satisfied. :)
339689
Yes, it's quite unclear, but I will try to guess.\n\n4a+b=38\n2a+3b=24\n\nDid you mean that we can multiply all but one equations in system in such way that coefficients with one variable ("a" for example) will be the same?\n\nExample: Multiplying second equation by 2.\n4a+b=38\n4a+6b=48\n\nNow we can subtract one equation from the other(s) and chosen variable ("a" in our case) will present only in one equation.\n\n4a+b=38\n5b=10\n\nNow we can get b from the second...\n\nb=2\n\n... and substitute it into the first.\n\n4a + 2 = 38\n4a = 36\na = 9\n\n\nThis method is the simplest example of Gaussian elimination (see attached article) and is often use to solve systems of linear equations.
768295
Using an equation is the lazy, mechanical way to do it. If you want to understand what's going on, factor it if possible.\n\nIf you *really* want to know what's going on, derive the quadratic formula yourself. It isn't as hard as it looks, and it can be done on one page.
638739
This is generally used for answering or solving problems.\nFor example if you do something like:\n4sin^2(theta)-9cos^2(theta)=(2sin(theta)+3cos(theta))(2sin(theta)-3cos(theta)) \nYou may write "Using x^2-y^2=(x+y)(x-y)"\nHope this helps...
837315
We don't actually use vectors in our every day lives, though we learn all about them during our flight training. As far as algebra II, we never do any math which is that complicated.
74442
I recommend purlplemath.com.  i'm not sure how helpful it is overal, but i like how they explain matrix multiplication <http://www.purplemath.com/modules/mtrxmult.htm>.  you can also do a web search for the subject you have a problem with, there are plenty of sites.  and your teacher should love to help you.
159293
Depends on what you are analyzing.  Matrix algebra is used extensively in communications and signal processing applications.  Not very much, though, in financial applications.
228730
You can describe rotations and the effect they have on each point in the figure mathematically by means of simple trigonometric equations which can be condensed into a matrix. Imagine (or better, draw) a point on the plane in coordinate system X0,Y0, located at X0=1, Y0=0. Draw a line to the point from the origin. Now draw another coordinate system X1,Y1 with the same origin as X0,Y0 but rotated CW by an angle Theta. (Make Theta small, say 30 degrees.) What are the coordinates of our point in the new system? The answer is a function of Theta. We find that the point is above the X1 axis and nearer the Y1 axis. Specifically, X1 = X0*cosine(Theta) and Y1 = X0*sine(Theta). \nNow if you repeat this with a new point at X0=0, Y0=1, you find that X1 = -Y0*sine(Theta) and Y1 = Y0*cosine(Theta).\nNow the good part. You can put these four equations together to find X1,Y1 for any value of X0,Y0 (not just points located on one axis or the other). The result is\nX1=X0*cosine(Theta) - Y0*sine(Theta)\nY1=X0*sine(Theta) + Y0*cosine(Theta)\nNext you form a rotation matrix R from the Theta-dependent parts of these equations:\nR=[cosine(Theta)___ -sine(Theta)]\n__[sine(Theta) ___ cosine(Theta)] \nNow when you multiply any vector P0, representing any point in X0,Y0 coordinates, by this matrix R using the rules of matrix multiplication, you are actually using the above two equations, and the result is a vector P1 which is the same point represented in X1,Y1 coordinates. Expressed compactly, P1 = R*P0. P0 is said to be transformed by R to P1.\nOf course, this is a 2-dimensional transformation, and R is a 2-by-2 matrix. Sophisticated 3-D computer graphics use a 3-by-3 matrix implementing very similar equations to do 3-D transformations. This is how you can see convincing 3-D models of objects in rotation.
165029
And I assume that you know that after college you will never ever again use that worthless knowledge.  What scientist is going to be doing long hand algebra when they have a computer?  Ask your teacher who uses it on a daily basis and what percentage of the population that is.  Would you even want to as a job choice?  It's really a shame that schools require such nonsense.
1053962
I am assuming this is an "I hate math so I'm gonna complain about its lack of relevance" question and not a real question, but I'll answer it anyway.  I can't tell you every use of it, I suppose I've seen several, but here's one I see a lot.  If you have an object thrown in a trajectory, and you need to know when it will cross a certain height, or when it will be going a certain speed (I dunno, in case you're lobbing hand grenades or missiles someday when you're bored), the quadratic equation will come up in the solution, and it will give you BOTH of the answers, one for when the object is on the way up and one for when it's on the way down.
619394
Math is needed for lots of things!\nDo your homework!\n\nhttp://mathforum.org/dr.math/faq/faq.why.math.html\nThere are actually thousands of different jobs that require some knowledge of mathematics. Here are more than 30 firsthand accounts from Mathematicians at Work telling what some college math majors are doing, from an Air Traffic Control Systems Analyst and a Lawyer to a Data Capture Facility Troubleshooter on the Hubble space telescope.\n\nExactly How Is Math Used In Technology?, from the Mathematics Department of the British Columbia Institute of Technology, provides examples of math uses for biomedical engineering, food technology, building technology, chemical sciences, civil and structural engineering, graphics and computer-aided drawing (CAD), electronics, environmental health, mechanical engineering, mining technology, nuclear medicine, occupational health, petroleum technology, prosthetics, forestry and wildlife, robotics, and surveying.
20441
Linear algebra deals with linear vector spaces. Operations on linear vector spaces are limited to additon of two vectors and multiplication of a vector by a constant. Matrix algebra is a subset of linear algebra.\n\nIf X, Y, and Z are vectors, aX + bY = Z has meaning\nbut aX^2 + bY^2 = Z does not.
753930
The most intuitive way to answer is to use Gauss-Jordan elimination, as described below.\n\n\nw + x + y + z = 24\n3w + 3x + 3y + 3z = 72\n3w - 2x - 3y + 3z  = -9\n5x + 6y= 81\n\nw + x + y + z = 24\n5w + 5x + 5y + 5z = 120\n5w + 3x - 2y - 2z  = 4\n2x + 7y + 7z = 116\n\nw + x + y + z = 24\n2w + 2x + 2y + 2z = 48\n2w + 4x + 4y - 5z  = 22\n-2x - 2y + 7z = 26\n\n2x + 7y + 7z = 116\n-2x - 2y + 7z = 26\n\n4x + 9y = 90\n5x + 6y= 81\n\n20x + 45y = 450\n20x + 24y = 324\n21y = 126\n\ny = 6\n\n4x + 9y = 90\n4x + 54= 90\n4x  = 36\nx = 9\n\n2x + 7y + 7z = 116\n18 + 42 + 7z = 116\n7z = 56\nz = 8\n\nw + x + y + z = 24\nw + 9 + 6 + 8 = 24\nw = 1\n{w,x,y,z} = {1,9,6,8}\n\nAnother method is to put the coefficiants into a matrix, and put it into reduced-row echelon form.\n\n|1 1   1  1  24|\n|3  -2 -3 3 -9|\n|5  3  -2 -2 4|\n|2  4  4  -5 22|\n\nIn RREF...\n|1 0 0 0 1|\n|0 1 0 0 9|\n|0 0 1 0 6|\n|0 0 0 1 8|\n\nThese are all new valid equations, just in a much nicer form. Specially, 1w+0x+0y+0z=1, etc.\nThis tells us that w=1, x=9, y=6, and z=8.\n\nAlso, you could use Cramer's rule with these equations and get the same answer, but I will not demonstrate that one.
958006
in order to solve the system of equations you can do one of two things.  The easiest thing to do is to set the two equations to be equal. i.e. \n\nsince y=2x and y = -3x+5, then 2x=-3x+5.  In solving for x you will find that 5x=5 or x=1.  Then you can plug your resulting x back into the equation to get y=2(1) =2.  The main thing you are trying to do is get one of your variables to be equal to some combination of your other variables.  For example, if you are trying to solve 3y+2x-1=5x+3 and 6y=2x+7.  The first thing you want to do is to get a single variable by itself on one side of an equation.\nLet's start with the first equation, 3y+2x-1=5x+3. You would try to group the y terms by themselves on one side of the equation, an group the x terms and constants on the other side of the equation.  In this example, in order to group the terms correctly, you would have 3y=3x+4.  Then solve for y by itself by dividing both sides by 3.  The result is y=x+4/3.  You take this result and substitute for y in the second equation, 6y=2x+7.   You will get 6(x+4/3)=2x+7.  Then you solve for x by itself.  6x+8=2x+7\n4x=-1;  x=-1/4.  Then you can substitute this result back into either of your original equations to produce your solution for this system.  6y=2(-1/4)+7 => 6y=13/2 =>y=13/12.  In order to check your answer, you can graph the two linear equations.  Where the two lines intersect is the solution to your system.\n\n\nIf you are looking for a more advanced way to solve a system of equations, then you may want to consider using an augmented matrix.  Rearrange your equations so that you have only variables on one side of your equations, and only constants on the other side of your equations, then sole the system of Ax=b.  The matrix A is the coefficients of your variables, and b is a vector of your constants.  x is a vector of your variables.  Augment the matrix of your coefficients with your constant vector and do Gaussian Elimination until the matrix is in reduced row echelon form.  This will provide the exact solution to the system of equations.
811494
linear equations are used quite frequently in real life. a person wid not a deep kmowledge of mathematics also uses them.\nfor eg:\n1.   our daily budget wid income to b spent as 'm' for 5 commodities \n      namely a,b,c----------j nd their prices p1,p2,p3,----------p10 is a linear equn.\n                  a.p1+b.p2+----------------+j.p10=m\n\n2.   also the process of cost calculation in firms require them\n      as 'w' being d wage rate of labour and a value r as raw material cost. the equn becomes-\n                  l.w+r=cost, where l is d no. of labour hired\n\n\nmany other simple examples can b quoted.