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Matrices

Similar matrices and trace proof

(See attached file for full problem description with symbols) --- If A and B are matrices over the field F, show that the Now show that similar matrices have the same trace. Recall: Let A and B are matrices over the field F. We say that B is similar to A over F if there is an invertible matrix P over F such that . -

Matrix relative to a basis for a linear transformation.

--- Let be the linear transformation defined by . a) If is the standard ordered basis for and is the standard ordered basis for what is the matrix of T relative to the pair b) If and , where , , , , what is the matrix T relative to the pair --- See attached file for full problem description.

Parity check code-Generating matrix

I need help with writing a program that will generate message words (in 0's and 1's) and then compute the code words (in 0's and 1's). Ex: Generating Matrix for the (3,4) Parity check code: 100 1 010 1 001 1 derived from using the identity matrix and then solving for x,y,z in the 4th column Message words Code w

Prove the uniqueness of I, the n x n identity matrix.

Prove the uniqueness of I, the nxn identity matrix.

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

Find the equivalent first-order system for second order equation

Find the equivalent first-order system (that is, find the matrix A and the vector R of dv/dx = Av + R) for the second order equation: u'' + (x^2)u' + (x^4)u = 1/(1+x^2) Please see the attached file for the fully formatted problems.

See attachment

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

Matrices : Find distinct, real eigenvalues.

Find distinct, real eigenvalues. X' = (10 -5) (8 -12) X

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 Mathematics : Integer Algorithms, GCD, Solving Congruences and Diagonal Matrices

4. Describe an algorithm that takes as input a list of n integers and produces as output the largest difference between consecutive integers in the list. Integers 28. What is the greatest common divisors of these pairs of integers? a) 22 * 33 * 55, 25 * 33 * 52 b) 2 * 3 * 5 * 7 * 11 * 13, 211 * 39 * 11 * 1714 c) 17, 17

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 : Area of Parallelogram, Perpendicular Vectors , Angles Between Vectors, Orthogonal Vectors and Determinants

1. For vectors v and w in , show that v - w and v + w are perpendicular if and only if . 2. Let u = (-3, 1, 2), v = (4, 0, -8), and w = (6, -1, -4) be vectors in . Find the components of the vector x that satisfies 2u - v + x = 7x + w. 3. Find a non-zero u vector such that satisfies the following. a. u has the same d

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

Systems of Differential Equations : Fundamental Matrix, Linearly Independent Solutions and Vectors,

Please see the attached file for the fully formatted problems. I need: (c) on #4 (c), (d) and check (b) on #6 (e) on #7 For this to help me with the test coming up I will need all work and answers,

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 &#8594; 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

Matrix: Find the Values that Make the Determinant Equal to Zero

Determine the values of r which det(A-rI)=0 A=[3,3;2,4].

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

System of 3x3 equations with row operations

Solve each system of equations using matrices(row operations). Have to see step by step of what is going on. x + 4y - 3z = -8 3x - y + 3z = 12 x + y + 6z = 1

Nilpotent of a Matrix

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

Finding Inverse of a Matrix Using Elementary Transformation

Linear Algebra Matrices Inverse of a matrix and Elementary Transformation of a matrix Find the reciprocal (inverse) of the following matrix by using the Elementary Transformation of a matrix: A = [0, 2 , 1; 1 , 3 , 2; 4 , 1 , -3]

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