### Matricies to solve equation

Please help with attachment

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Please help with attachment

(a) List the ordered pairs that belong to the relation. My ANS: (a,a),(b,a)(b,b),(c,a),(c,b),(c,c),(d,a),(d,b)(d,d) (b) Find the (boolean) matrix of the relation. < my answer file attached as Mr.jpg> I did review another answer posted along the same question, but uses a different shape. I think my matrix is correct bas

| 0 2 3 | | 0 1 0 | | 1 5 7 |

|3 x | =2 |1 1 | keywords: solve, evaluate, evaluating

(See attached file for full problem description) --- Suppose that A, B, and AB are normal matrices. Prove that BA is also normal. Here some hints: the trace of matrices can be used in clever ways to prove equalities. Note that tr(A+B)=tr(A) + tr(B), tr(AB)=tr(BA) for any square A and B, and tr (C*C) 0 with equality if a

4.1. If A, B are bounded operators on H, show that (AB)*= B*A*. Even if A, B are both self-adjoint, the product AB may not be.

Find the orbit and stabilizer of the 2 X 2 matrix M under the action of multiplication of M by the matrices in GL_2(R), where the top row of M is (1 0) and the bottom row is (0 2). [That is, m_11 = 1, m_12 = 0, m_21 = 0, and m_22 = 2.] See attached file for full problem description.

(See attached file for full problem description) --- a) Recall the following definitions of the multiplicative groups GLn(k) and SLn(k) over a field k: GLn(k)={invertible n x n matrices over k} SLn(k)={A in GLn(k) such that the determinant of A=1} Prove th

Let A be an n invertible matrix. Define T: Mnm--> Mnm by T(B)A^-1 BA. i) Is T a linear operator? ii) Is T one-to-one?

Show that Jordan block (matrix) is defective. Please see the attached file for the fully formatted problems.

This has multiple choice answers as well as some that need some written work. The attachment shows exactly what it needs. Thanks for the time. Please Answer the following questions, some are multiple choice, others require some work. 1. Write the augmented matrix for the given system: 2. Use the system in pro

1. Let's define the operator M as follows: Mu = f(x) u'' + g(x) u' + h(x) u Now define the adjoint of M as M* and let M*v = (fv)'' - (gv)' + hv = fv'' + (2f' - g)v' + (f'' - g' + h)v Show that (M*)* = M

Show that any matrix A can be written as a sum of rank-1 matrices. And show how these rank-1 matrices can be chosen so that only r of them are necessary (where r=rank(A)).

Each of the following expressions defines a function D on the set of matrices over the field of real numbers. In which of these cases is D a 3-linear function? Justify your conclusions. a) D(A) = A11 + A22 + A33 b) D(A) = A11 A22 A33 Recall: Let K be a commutative ring with identity, n a positive integer, and let D

Coding Theory Program -------------------------------------------------------------------------------- I have attached the specifications --> Program2.doc. I need it written in Java. I have also attached --> Program 2 Defined This will help with understanding the program. The words must be generated using matrix mult

Determinates a) In the accompanying figure, the area of the triangle ABC can be expressed as area ABC = area ADEC + area CEFB - area ADFB Use this and the fact the area of a trapezoid equals 1/2 the altitude times the sum of the parallel sides to show that: (see attached filed) Note: In the derivation of this form

--- 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.

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 nxn identity matrix.

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.

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

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

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

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

(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). ---

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

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

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,

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.

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