### Matrices : Show the Jordan Block is Defective

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

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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

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

Use Matlab commands lu(A) and A b to solve the following problem. I need the answer as a matlab file, or at least as a copy of the print-out of the input and output lines. Let 2 2 -4 10 A = 1 1 5 b = -2 1 3 6

(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 . -

--- 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.

Prove the uniqueness of I, the nxn identity matrix.

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

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

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.

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

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

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

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 : 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}

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

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

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

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

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]

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

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).

If ' is a symplectic matrix show that det ' = 1. Also prove that....where P(...) = det(,,,) is the characteristic polynomial of '. Finally, if ... is an eigenvalue with multiplicity k of ' then the same is true for...

Prove that addition modulo n, written +n is: 1) associative 2)comutative there are two ways to prove these properties. each way requires a definition or two: 1) for n≥2, 0≤a, b≤n+1 a+n(written as a power in a corner downside, but dont know how to put it tho) b={condition 1 - a+b if a+b<n;condition 2 - a

Q1. Suppose An is the n by n tridiagonal matrix with 1's everywhere on the three diagonals... Let Dn be the determinant of An; we want to find it. (a) Expand in cofactors along the first row of An to show that Dn = Dn-1 - Dn-2 (b) Starting from D1 = 1 and D2 = 0 find D3, D4, ..., D8. By noticing how these numbers cycle a

X + 2y + z = 0 -3x + 3y + 2z = -7 4x - 2y - 3z = 2