Matrix

Question: Matrix???? which matrix movie did u like the best. me personally, i like the first one. which one do you like and why??

Answer: From a sci-fi action perspective, I thought Reloaded was the best. The interstate highway chase, the fight with all of the Agent Smiths, and the brief scenes with Daniel Bernhardt (a gifted martial artist) made it visually stunning. And Monica Belluci is such a fox. Of course, I give the original the edge for being just that, "original".

Question: How do the characters in the Matrix do all those superhuman abilities? I've wondered how do Neo and the other Matrix characters do what they do in the movies. If it's a sci-fi, there's got to be a universal explanation for what they do right? Here are examples: 1. The Twins turning into ghostly beings in the Matrix Reloaded 2. Neo flying in the Matrix and Matrix Reloaded. In the Matrix Reloaded, Neo makes a pulse on the ground before he flies. This could be useful in finding a method of using superhuman abilities inside a virtual reality.

Answer: The Twins were rogue programs that worked for the Merovingian. Any rogue programs aren't bound by the same rules as other programs within the Matrix. As for Neo's flight ability aside from being "The One" (meaning he was born into the Matrix and is able extend that power and ability beyond the Matrix to its source and change the Matrix to how he sees fit etc) Being freed from the Matrix means that you are aware that it isn't real and you can open your mind and do things that would seem otherwise impossible. eg flight, superhuman strength, bullet dodging etc.

Question: What are the dimensions of the resulting matrix found by multiplying a 2 by 3 matrix and a 4 by 2 matrix? What are the dimensions of the resulting matrix found by multiplying a 2 by 3 matrix and a 4 by 2 matrix? 2 by 2 3 by 4 2 by 4 this is not possible thanks!

Answer: 2×3 by 4×2 is not possible Let A = n×m Let B = m×p A·B = n×p The inner dimension must be the same.

Question: How do I express a matrix as a product of elementary matrices by reducing it to reduced echelon form? The matrix A is 1 3 4 10 And i you can get reduced echelon form as follows: 1 3 4 10 R2: R2 - 4R1 which gives 1 3 0 -2 R2: -0.5R2 which gives 1 3 0 1 which is reduced echelon form. But how do you get the product of the matrix A from this?

Answer: Every time you do an elementary row operation, you are actually multiplying the original matrix by a corresponding elementary matrix! To create an elementary matrix given the row operation, you just act on the appropriately sized identity matrix (in this case, 2 by 2) in the same way. For your example, applying R2: R2 - 4R1 to 1 0 gives 0 1 1 0 -4 1. This last matrix is the corresponding elem. matrix to your row operation. Call this E1 Likewise, applying R2: -0.5R2 to 1 0 gives 0 1 1 0 0 -.5 We'll call this E2. So, your reduced echelon matrix should be equal to (E2)(E1)(A). Note the order of the elementary matrices is multiplied by A to its left in reverse order! Double check (multiplying left to right): 1 0 * 1 0 * 1 3 0 -.5 * -4 1 * 4 10 equals 1 0 * 1 3 2 -.5 * 4 10 equals 1 3 0 1 as required!

Question: How do you unplug yourself from the Matrix? As you may already be aware the Matrix is a computer generated world that we are all plugged into. In the Matrix we are all slaves to the system and not in charge of our own destinies. How can you free your mind from the Matrix? Is it possible to transcend the system and status quo? For info, I understand that the Matrix film is a work of fiction. But I am interested in its philosophical implications.

Answer: If you are asking the question, then you have already allowed yourself the process of unplugging. Never fail to ask questions to the everyday mundane challenges that always seem the same. Create a destiny of your own choosing and follow the govern rules of morality vs. normality.

Question: How to find the inverse of a matrix containing complex imaginary numbers? Is the method for doing this the same as if the matrix contained real numbers? This is how I would find the inverse of a matrix with real numbers A. Make the augmented matrix [A|I] and then use row reduction to change it to [I|B] B being the inverse of A. Basically my question is, can you do this with imaginary complex numbers?

Answer: Yes. Imaginary and complex numbers obey the same rules of arithmetic as real numbers.

Question: How much would it cost to upgrade from the pantech matrix to the matrix pro? How much would it cost to upgrade from the pantech matrix to the matrix pro for At&t

Answer: i had it just say if u have insurance that it broke they will ask u what phone it is and just say a matrix pro withn 1to2 days it will be at ur house.. :)

Question: What is the solution for the determinant of an identity matrix? Is the determinant of a 2x2 identity matrix found in the same way in which that of other matrices is found? Or, is the fact that it's an identity matrix in any way change the outcome? Thanks for the help.

Answer: The determinant of an identity matrix of any dimension = 1 Yes, you find the determinant the same way as you find for other matrices. For more problems on matrices, visithttp://onlinehometutors.com/Free-Algebra-Worksheets.php

Question: How to determine the transition matrix for this Markov chain? Consider two urns A and B containing a total of N balls. An experiment is performed in which a ball is selected at random (all selections equally likely) at time t(t = 1, 2,..) from the collection of all N balls. Then an urn is selected at random (A is chosen with probability p and B is chosen with probability q and the ball previously drawn is place in this urn. The state of the system at each trial is represented by the number of balls in A. --> Determine the transition matrix for this Markov chain.

Answer: Dear carnation, Let S be the current state (i.e., the number of balls in urn A), so S is in {0, 1, 2, . . . , N}. Then the (N + 1) by (N + 1) transition matrix can be defined by P(S → S - 1 | S) = q S / N, P(S → S + 1 | S) = p (N - S) / N, and P(S → S | S) = 1 - [q S + p (N - S)] / N, where P(b → a | b) represents the probability of moving from the "before" state b (i.e., at time t), to the "after" state a (i.e., at time t + 1), given the system is currently in state b.

Question: What is the easiest way to solve a matrix problem in algebra? I am currently enrolled in intermediate algebra class. I found it to be interesting until we discussed matrices! I do not know how to solve it. I understand the goal of having the main diagonal line to be 1 and three zeros. However, I find it hard. Is there an easy way to solve a matrix?

Answer: That is the easy way. Wait until you had to solve 5 unknowns with 5 equations. Try to do without using matrix, and you will how annoying that is. For example, if you 2 equations, and you need to solve for 2 unknowns, then it's not worth it to use matrix, since substitution or cancellation of variables will get the job done. Not everything in life can be done by shortcuts, and that statement is true for mathematics too.

Question: How do I contruct a matrix that acts on a vector x to make it parallel to another? How can you construct a nonzero 2x2 matrix A, so that Ax where x is is always parallel to <1,2>. Could you only do this by considering <0,0> as parallel to <1,2>?

Answer: No, that can be done with infinitely many matrices in the form: (a, b) (2a, 2b), /a,b - arbitrary/ Now AX = (ax1 + bx2, 2ax1 + 2bx2) || (1, 2) /understand column-vectors here!/ If You denote as usual the 4 elements of A as a_11, a_12, a_21, a_22 and express a_11*x1 + a_12*x2 = k a_21*x1 + a_22*x2 = 2k /k - arbitrary, (k,2k) || (1,2)/ That leads to (2a_11 - a_21)*x1 + (2a_12 - a_22)*x2 = 0, the latter to be always satisfied requires both expressions in parenthesis to be 0, so the A's 2nd row must be twice the 1st.

Question: How do I find the matrix representation for the orthogonal projection onto vector v? Say I have a vector [1 3]^t. How do I find the matrix representation for Pv by finding what it does to the standard basis vectors, e1 and e2?

Answer: I'm not sure what you are asking. If you want to project a vector V onto a standard basis composed of E1 and E2, then: If E1 and E2 are orthonormal, then any vector V = (V.E1)E1 + (V.E2)E2. Notes: - E1 and E2 are orthonormal if they are perpendicular and have length 1 http://en.wikipedia.org/wiki/Orthonormal_basis - (A.B) means the dot product of the vectors A and B. The results is a scalar that gives the length of component of B parallel to A times the length of A (which is equal to the length of the component of A parallel to B times the length of B) http://en.wikipedia.org/wiki/Dot_product If, on the other hand, you have some linear transformation, then you can find its matrix representation by seeing what it does to E1 and E2. Let the transform be T: T11 T12 T21 T22 Then since E1 is (by definition) <1, 0>, if T(E1) = , then: T11 = X1 and T21 = Y1 Similarly, since E2 = <0, 1>, if T(E2) = you get: T12 = X2 and T22 = Y2

Question: What shampoo to use after matrix opti smooth straghtening? Just had my hair chemically straightened and the hairdresser told me not to use my usual shampoo and i should only use matrix products, has anyone else had this done and what have u used on your hair afterwards?

Answer: Tresemme straightening shampoo

Question: How do you triangularise a square matrix? I'm having difficulty with triangularising square matrices. Unfortunately the lecturer ran out of time today, and so wasn't able to do any examples of how to triangularise a square matrix, and I have some work to hand in tomorrow and am very stuck! I would really appreciate it if anyone could give me an example of how to triangularise a square matrix, or if you could recommend any websites that show how you would go about this. Thanks for letting me know about the elementary row operations. Do you know if there is any way to find an invertible matrix P such that P^(-1)AP is triangular, where A is the original matrix (assuming that it's minimal polynomial is the product of linear factors)? I'd really appreciate it if you could point me in the right direction! Thanks!

Answer: here's an example we want to reduce a matrix to u/t form 1 10 -3 r1 1 10 2 r2 1 4 2 r3 1 10 -3 0 0 5 0 -6 5 r2-r1 r3-r1 1 10 -3 0 -6 5 0 0 5 interchange rows 2 and 3 upper triangular form this is known as gaussian elimination and is used in solving systems of equations go to the site: http://mathworld.wolfram.com/GaussianElimination.html this gives a good example you can also get help with other matrix operations at this site,plus access to the integrator as well i hope that this helps

Question: How do I find a diagonal matrix similar to another matrix? Let J denote the nxn matrix over R whose entries are all equal to 1. Show that J is diagonalizable and find the diagonal matrix similar to J. What is the characteristic polynomial of J?

Answer: J=( n 0 0 0 0 0 0 ... } ...{ 0. 0 0 0 0 0 0 ...} ...{ .......................} ...(..............0 0 0 0} The characteristic polynomials are (n - x)x^(n-1) = 0

Question: How to find the square root of a matrix? I know how to find the square or cube of a matrix (multiply the matrix with itself as many times as needed). But finding the square root of a matrix got me stumped. How do you find the square root of a matrix?

Answer: What you have to do is diagonalise the matrix (it gets trickier if you can't diagonalise it, but a similar method works using the Jordan canonical form), that is, write it in the form A = PDP^-1, where D is a diagonal matrix. You can then raise D to any power you like by raising the individual entries by the same power (so to get sqrt(D) you just take the square root of all the diagonal entries). Then A^p = P(D^p)P^-1. It works because if, for example, you take A^(1/2) = P(D^(1/2))P^-1, you can multiply two of them together and get P(D^1/2)P^-1 * P(D^1/2)P^-1 = P(D^1/2)(P^-1 * P)(D^1/2)P^-1 = P(D^1/2)I(D^1/2)P^-1 = P(D^1/2)(D^1/2)P^-1 = PDP^-1 = A.

Question: matrix?!?!?!?!? ive herd of matrix sleek look and people say it workz reely well. i realy dont want to pay 20 bucks for freakin shampoo. arent there any other good products that are cheaper that work just as well?

Answer: the product really is worth the money, i love the matrix sleek look line.