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Matrices

Real-World Augmented Matrix Problem

From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material. In your own words, please post a

Matrix formulation for interpolation of data

In the attached article, the author proposes a way to interpolate quarterly values when only annual values are available. The only page of this article which is useful for this problem is page 66 (or the second page in this attachment). I am trying to understand the very first step, which is how to get from the statement of t

Properties of Matrices and Vectors

Please show all work for attached problems. 1. Let A, and B be skew- symmetric matrices. Prove that AB is skew symmetric if and only if AB = -BA 2. IF possible find a vector u=(a,b,c) where a, b, c are not all zero so that "u" is orthogonal to both vectors: x= (1,2,1) and y = (1,-1,1) The following are proof questions.

Question on chromatic number of graph, adjacency matrix and list.

Please see attached questions. This is three questions. Question #1 - find the chromatic number of the graph. Question #2 - It might be supposed that if a graph has a large number of vertices and each vertex has a large degree, then the chromatic number would have to be large. Show that this conjecture is incorrect by co

Solve

I have attached the problems. 1. Write the augmented matrix for the given system: Answer HTML Editor 2. Use the system in problem #1. Without interchanging any of the rows in the augmented matrix, what is the first value which will be replaced with zero when using the Gaussian Elimination method? A. -1 B

Vector field proof

Please solve attached part b. Suppose that x<-->A(x) is a smooth mapping from a neighborhood U of R^n containing 0 into the SO(n) matrices, defined by the relations....Show that for any vector field X on U.....

Rotation matrix

Show that if q is an element of Reals, then the operator T : Reals^2 -> Reals^2 given by T ( x , y ) = ( x* cos q - y * sin q , x * sin q + y * cos q) has no real eignvalues unless T = I. I is identity.

Vectors, matrices, and bases

Please show all work. Thanks. See attached for proper formatting Question 1 Let B={v1,...,vn} be a basis of a subspace V of Rnx1. Let x be the nonzero vector x=a1v1+...+anvn for scalars ai. Let C={x, v2,...,vn}. a) Show that if a1 is not equal to 0 then C is also a basis. b) Show that if a1 =0 then C is not a basis.

Matrix Theory: Linear Combinations and Orthonormality

Three vectors v1, v2 and v3 are given (see attachment). 1. show that v1, v2 and v3 are orthonormal 2. vector w is given (see attachment). Find <w,v1> , <w,v2> and <w,v3> 3. Is w a linear combination of v1, v2 and v3? If yes, what is the combination? If not, why not? 4. is the given vector u (see attacment) a linear comb

Matrix problem

Four theaters comprise the Cinema Center: Cinemas I, II, III, and IV. The admission price for one feature at the Center is $2 for children, $3.50 for students, and $5.75 for adults. Suppose that on a particular Sunday 240 children, 100 students, and 75 adults attended the evening show in Cinema I; 60 children, 240 students, and

Matrices and word problems

A contractor employs carpenters, electricians, and plumbers, working three shifts per day. The number of labor-hours required for carpenters in shift 1 is 40 hours, electricians in shift 1 is 28 hours, and plumbers in shift 1 is 9 hrs. The number of labor-hours required for carpenters in shift 2 is 18 hours, electricians in shif

Gauss-Jordan elimination

Set up the augmented matrix while using Gauss-Jordan elimination to solve the system. Provide some notation showing how to proceed from one augmented matrix to the next. 3x-6y+9z=0 4x-6y+8z=-4 -2x-y+z=7

Matrices and Vectors

Please see the attached file. Find a matrix A which takes...Is it possible to find a matrix C which takes...

Eigenvalues, multiplicities, and eigenspace

Please see the attached problem. Thank-you Suppose that A = S&#923;S-1 where S = and &#923; = Find the eigenvalues of A. For each, give the algebraic multiplicity, geometric multiplicity, and describe the eigenspace.

Diagonalizing matrices theory

Please see the attached problem. Thank-you Diagonalize the following matrices (if possible). You may use technology to find the eigenvalues, to row reduce matrices, and to find inverses, but that's all. Show your work. Think about easy ways to check your answers. (a) M= (b) N=

Matrix subspace theory

Please see the attached file thank-you for your help. Let A be an n x n matrix, and suppose "T" is a subspace of . Define A(T) to be the set that results from multiplying "A" times vectors in "T" in all possible ways; that is, . (a) Show that A(T) is also a subspace of . (b) For the particular case that A = And T

Invertible matrix proof theory

Please see the attached file. Thank-you for your help. Suppose that u1, u2, . . . , ut are vectors in Cn (complex number) which are linearly independent. (a) Also suppose that "M" is an n x n matrix that is invertible. Show that Mu1, Mu2, . . . , Mut are linearly independent vectors. (b) This isn't true when "M" is

Eigen value and invertible matrix

(a) Suppose that "A" is a square matrix which is not invertible. Prove that zero is an eigenvalue for "A". (b) Is the converse true? That is, is it true that if zero is an eigenvalue of "A" then "A" is not invertible? Justify your answer.

Matrix theory and analysis: Invertible matrices

Please see the attached document for homework specifics. Thank-you. Suppose that A and B are invertible n x n matrices A. Show that if c &#8800; 0, then cA is invertible. Justify your answer, using the definition of an invertible matrix. What is (cA)-1 ? B. Must A + B be invertible? If so, show that is it; if not

Coding

Please see attached files ? Encode the message "CALLMESOON" as a 2X5 matrix, using this matrix: ? Encode the message "HELPISINTHEMAIL" as a 3X5 matrix, using this matrix:

Matrices

Please see attached file Compute the indicated matrices...

Vectors spanning C and linear independence

Please see the attached document regarding homework specifics. Thanks so much for your expertise. Do the vectors v1, v2, v3 span C? Justify your answer. Are the vectors v1, v2, v3 linearly independent?