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Matrices

Find the determinant of 2x2 matrices

Q: Find the determinant of these 2x2 matrices. (a) mat[4 3; -2 9] (b) mat[5 -7; 4 12] Please see the Word document for a cleaner version of the problem.

High School Algebra Questions

4. dependent system a) a system that is dependent b. a system that depends on a variable c. a system that has no solution d. a system for which the graphs coincide 8. Matrix a) a movie b) a maze c) a rectangular array of numbers d) coordinates in four dimensions 12. Sign array a) the signs of the entries of

Inconsistent Systems and Augmented Matrices

Inconsistent system a. a system with no solution b. a system of inconsistent equations c. a system that is incorrect d. a system that we are not sure how to solve Augmented Matrix a. a matrix with a power booster b. a matrix with no solution c. a square matrix d. a matrix containing the coefficients and constants of

Graphs : Adjacency Matrix, Order and Valency

Let A be the adjacency matrix of a regular graph of order v and valency k. Let J be the all-ones matrix of the same order. Show that A*J = J*A = K*J "Definition 2.1 A graph r with adjacency matrix A = A(r) is called regular if there exists a natural number k such that AJ = JA = kJ. The number k is called valency of r."

Linear binary code

You can not use the definition Hermitian inner product to solve this problem. You need to use the definition of weight. We need to generalize the equation. 1-Define the product, x*y , of two binary vectors of the same length to be the vector whose ith component is the product of the ith components of x and y. Show tha

Binary Hamming Code Vectors

See attached file for full problem description. 7. The parity check matrix of a binary [n, k, d] = [15, 11, 3] Hamming code whose columns are in numeric order is a) Find the corresponding generator matrix. Use the method of permuting and unpermuting the columns for the [7, 4, 3] binary Hamming code. b) Encode the

Standard form

See attached file for full problem description. 6. Let be the binary repetition code with parameter [n, k] = [12, 4]. a) Give a generator matrix for that is in standard form. What does standard form means? b) Give a parity check matrix for that is in standard form. c) What is the minimum distance of ? d)

Binary linear block

See attached file for full problem description. 3. Let be a binary linear block code with parameter [n, k] = [6, 3] which has as its generator matrix. Assume that the first three bits of each codeword are the information bits. a) Find a generator matrix for that is in standard form. What does standard form mea

Orthogonality of a Generator Matrix of a Binary Block Code

Please see the attached file for the fully formatted problems. 4. Let be the generator matrix of a binary block code . a) Show that each row of G is orthogonal to itself and to each of the other rows of G. b) Show that each codeword in is orthogonal to itself and to every other codeword in . Note: Use part a)

Binary Hamming code

1-Define the product, , of two binary vectors of the same length to be the vector whose ith component is the product of the ith components of and . Show that wt ( + ) =wt ( ) +wt ( ) - 2wt ( ) . wt means weight. 2. Suppose that a binary Hamming code is modified by adding an additional check bit to each codeword. This ad

Parity check matrix

1.- Find a parity check matrix for the [12,4] repetition code. Can you expalin what does mean repetition code and the parity check matrix? 2.- Show that the complement of each codeword in the [12,4] repetition code is again a codeword. Note: do not do this problem by checking all the sums of codewords. Please Can yo

Matrix Functions

1.Consider the 2 functions f1(t) and f2(t); 1. f1(t) = { a1.e^ -2t for t>=0 and = { 0 for t<0 } f2(t) = { a2.e^ -t + a3.e^ -2t for t>=0 and = { 0 for t<0 } Find a1,a2 and a3 such that f1(t) and f2(t) are orthonormal on the interval 0 to infinity. 2. If Q is an n x n symmetric matrix and a1,a2 are such that 0 < a1I <

Matrices

These are problems from the text that were advised to study for the next exam. (see attachment for equations) 1) Determine the values of r for which det(A-rI) = 0 2) Verify that X(t) is a fundamental matrix for the given system and compute X-1(t). Use the result, x' = Ax, x(t0) = x0 to find the solution to t

Problem Set

5) Use cofactor expansion to find the determinant | 4 -1 1 6 | | 0 0 -3 3 | | 4 1 0 14| | 4 1 3 2 | 6)Find the characteristic equation, eigenvalues, and corresponding eigenvectors for A = 1 2 2 1 7) Answer True or False for the following statements: (True means always true; False means sometimes false). Ju

Vectors and Matrices : Operations and Transformations

1) Let u=(2,3,0), and v=(-1,2,-2). Find a) ||u + v|| b) ||u|| + || v || c) Find two vectors in R³ with norm 1 orthogonal to be both u and v d) Find norm of vector u / || u || 2) For which values of t are vectors u = (6, 5, t), and v = (1,t,t) orthogonal? 3) a) Find the standard matrix [T] for the linear tra

Solving Systems of Equations Word Problems and Matrix Inverses

6. How many 7-card hands are possible with a 52-card deck? 7. The owner of nuts2u snack shack mixes cashews worth $5.50 a pound with peanuts worth $2.30 a pound to get a half-pound mixed nuts bag worth $1.80. How much of each kind of nut is included in the mixed bag? 8. Determine whether the matrices are inverse. [5

Matrix

(See attached file for full problem description)

Hasse Diagrams

(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

Normal matrices

(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

Self-Adjoint Sets

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.