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    Triangles and matrices

    Researchers at the National Interagency Fire Center in Boise, Idaho coordinate many of the firefighting efforts necessary to battle wildfires in the western United States. In an effort to dispatch firefighters for containment, scientists and meteorologists attempt to forecast the direction of the fires. Some of this data can be

    Differential Equation and Matrix Determinant

    1.The ODE X"+ kX = 0 has different types solution depending on sign of k. We consider the three possible cases separately. k=0: X"=0 so that X(x)=Ao+Box, X'(0)=0 implies Bo=0 so that X(x)=Ao. Finally, X(1)=0 implies Ao=0 and there is only trivial solution X=0. The matrix has determinant e^mu + e^-mu= 2cosh.mu, which is

    Union, Intersection, Composition and Symmetric Different

    Let R1 and R2 be relations on a set A. represented by the matrices: M R1 0 1 0 M R2 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 find the matrices that represent ( show all work) a) R1 union R2 b) R1 intersection R2 c) R2 º R1 (composition) d) R1 º R1 (co

    Sovling Eigenvalues Problem

    For an n x n matrix A, show that if one or more of the eigenvalues is zero, A has no inverse. Also show that if, A does have an inverse, the eigenvalues of A^-1 are the reciprocals of the eigenvalue A.

    Discrete Math Definitions : Algorithm, Searching algorithm

    On the following terms could you please give my an English text description - in your own words. Thanks. 1. Algorithm: 2. Searching algorithm: 3. Greedy algorithm: 4. Composite: 5. Prime: 6. Relatively prime integers: 7. Matrix: 8. Matrix addition: 9. Symmetric: 10. Fundamental Theorem of Arithmetic: 11. Euclidean A

    Fundamental matrices

    (See attached file for full problem description with the matrix) --- a) Write the fundamental matrix for the system: b) Compute the exponential matrix where A is the matrix in part a). ---

    Vectors and Matrices: Matrix Operations

    1. Take the following three row vectors: A = (1, 3), B = (7, 9), C = (7, 2) 1. Find the column vectors V = AT, W = BT, X = CT 2. Create the Matrix D such that A is the first row, B is the second row, and C is the third row 3. Create the Matrix E such that V is the first column, W is the second column, X is the third column 4

    Matrices and Their Use in Coding and Encription

    The use of coding has become particularly significant in recent years. One way to encrypt or code a message uses matrices and their properties. We start with a message coded into matrix form, called A. Multiply A by another matrix B to get AB and send the message. a) What would we need to decode the message at the other end t

    Diagonal Matrix Representation, Standard Basis Vectors

    A linear mapping T : R2 -> R3 is defined on the standard basis vectors via T(e1) = (1, 0, 1) and T(e2) = (1, 0, -1) 1. Calculate T(3,3) 2. Find the dimension of the range of T and the dimension of the kernel of T. 3. Find the matrix representation of T relative to the standard bases in R2, R3. 4. Find bases {v1, v2}

    Diagonal Matrix Representation : Linear Mapping, Basis and Kernels

    A linear mapping T: R3 → R2 is defined on the standard basis vectors via: T (e1) = (0, 0), T (e2) = (1, 1), T (e3) = (1, -1) i. Calculate T(4,-1,3) ii. Find the dimension of the range of T and the dimension of the kernel of T. iii. Find the matrix representation of T relative to the standard bases in R3, R2. iv.

    Invertibility of Matrices

    Can you please explain to me why the columns of the nxn matrix A span R^n when A is invertible? I feel that if matrix A has columns that span R^n, then the inverse of A should likewise share that same characteristic, the spanning. But I'm not sure if that is a sufficient relationship. Can you give an example of matrix A spanning

    Parametric/simultaneous equations and matrices.

    See attached file for full problem description with diagrams and equations --- Parametric equations and matrices. The diagram below shows a line defined by the parametric equations , which crosses the x- and y-axes at the points (a, 0) and (0, b), respectively. The region marked A, is bounded by this line, the x- axes, th

    Duality Principal and Multiplying Matrices of Differing Size

    See the attached file for the full solution. 1) Please explain in your own words the duality principle. 2) The biggest problem I have with matrices is the multiplication. I get them right but I believe the confusion comes from the way it is set up. To be more clear the way it is set up as far as the rows and columns. If it is

    Nilpotent of a Matrix

    Linear Algebra Matrices (XII) Nilpotent of a Matrix Show that the matrix A = [8, 10 , -16; 32 , 0 , 0; 24 ,

    Generating seed values

    I am a licensed land surveyor in Illinois and Montana, and I write surveying software (I've been out of college for 20+ years). Currently, I am programming a 3D Conformal Coordinate Transformation, also known as the seven-parameter similarity transformation. I have the book "Adjustment Computations" by Wolf & Ghilani. Section 1

    Testing solutions

    The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. If there is anything unclear in the question, let me know. Thank you. The Rockmore Corp. is considering the purchase of a new computer....They test both computers' ability to solve the line

    Hubert Matrices Using Matlab

    C) The famous Hubert matrices are given by Hij= 1/(i +j - 1). The n x n Hilbert matrix Hn is easily produced in MATLAB using hilb(n). Assume the true solution of H,x = b for a given n is x = [1.. .. , 1]^T. Hence the righthand side b is simply the row sums of H, and b is easily computed in MATLAB using b=sum(hilb(n) 9'. Use your

    Gaussian Elimination and Operation Count

    Consider the problem Ax=b where A is a tridiagonal matrix. What is the operation count for the forward elimination and the back substitution steps of Gauss elimination in this case? Count add/sub and mult/div operations separately, then give the overall order of the total operations needed. (Use O(n^p) notation).