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Matrices

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

Matrices and scalars for inverse covariance

I am unclear as to how some scalars have been calculated. I know what the two vectors and the inverse covariance variance matrix are but please could you clarify the operations required to compute into a single number? There is also a set of data on page two that needs computing along with a general explanation of how to do it.

Linear Equations and Matrices

Gretchen Schmidt plans to buy shares of two stocks. One costs $32 per share and pays dividends of $1.20 per share. The other costs $23 per share and pays dividends of $1.40 per share. She has $10,100 to spend and wants to earn dividends of $540. How many share of each stock should she buy? Use the form of " AX=B " equation

Matrices and their Applications

Please help me by showing how these problems on matrices are worked out. (See the Attached Questions File) Answer all questions and show work 1. Find: 2. Find the inverse of: 3. Compute the transpose of A = 4. Introduce slack variables and set up the initial tableau. Do not solve. M

Gaussian Elimination with Scaled Partial Pivoting

Please see attached problem (both Word and pdf version attached). Solve the system 3x1 13x2 | 9x3 | 3x4 = 19 6x1 | 4x2 | x3 18x4 = 34 6x1 - 2x2 + 2x3 + 4x4 - 16 12x1 - 8x2 + 6x3 + 10x4 - 26 by hand using scaled partial pivoting. You may only do the operations on rows that are permitted in Algorithm 6.3 You should nev

Inverses

In your own words can you explain to me how inverses are used to solve linear systems?

Construct the transition matrix.

4. A city is served by three cable TV companies: Xcellent Cable, Your Cable, and Zephyr Cable. A survey of 1000 cable subscribers shows this breakdown of customers from the beginning to the end of August. Company on Company on August 31 August 1 Xcellent Your Zephyr Xcellent 300 50 50

Augmented Matrix and a Real World Problem

From the following augmented matrix (see attachment), 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.

Scalar matrices with a different from zero.

Problem 1: Show that the center of GL(2,R) is the set of all scalar matrices aI with a different from zero. Problem 2: Prove that no pair of the following groups of order 8, I8; I4 x I2; I2 x I2; D8; Q, are isomorphic.

Gauss-Jordan Method

Gauss-Jordan method 1. x+y+z=7 x-y+2z=7 2x + 3z+=14 a. 3z+14 z 2 2 z b. -3z - 14z 2 2 z c. -3z +14 z 2 2z d. -3z + 14 2 2z,z 2. 2x -5y +z = 11 3x + y - 6z =1 5x - 4y -5z = 12 a. -29z + 16 15z-31 17 17 z b. 29z +16 15z +31 17 17 z

Matrices and Systems of Equations

1. To raise money, the local baseball teams decided to sell team logo hats (H) and T-shirts (T). The league director decided to hold a contest among the teams to see which team can raise the most money. The contest lasted for 3 weeks. Here are the results of the first 2 weeks. The numbers represent the number of hats and T-shirt

Provide an example of a matrix that has no solution.

Assistance with Matrices Please see attachment. Provide an example of a matrix that has no solution. Use row operations to show why it has no unique solution. Also, some matrices have more than one solution (in fact, an infinite number of solutions) because the system is undetermined. (In other words, there are not enough co

Matrix Rank and Consistent Systems of Equations

We are not using calculator so the steps need to be shown to the solution. 1) The augmented matrix of a linear system has been transformed by row operations into the form below. Determine if the system is consistent. 2x - y = 7, x + 4y = -5

Matrices and Solutions

Matrices are the most common and effective way to solve systems of linear equations. However, not all systems of linear equations have unique solutions. Before spending time trying to solve a system, it is important to establish whether it in fact has a unique solution. Provide an example of a matrix that has no solution. Use

Invertible Matrices and Orthonormal Basis

1. (10 pts) Prove or disprove: Let {v1, . . . , vn} be a basis for Rn. If A is an invertible n × n matrix, then {Av1, . . ., Avn} is also a basis for Rn. 2. (20 pts) In P3, define the function ..... (a) Show that p, q is an inner product. (b) Find an orthonormal basis for P3. (c) Express 7x2 − 2 as a linear comb

Linearly Independent Vectors and Invertible Matrices

If you let {v1, v2,...,vk} be linearly independent vectors in and A & B are n x n matrices. If you assume A is invertible how would you show that {A(v1), A(v2,)...,A(vk)} are linearly independent? Also, if you know that {v1, v2,...,vk} are linearly independent and {B(v1), B(v2,)...,B(vk)} are linearly independent, how do yo

Matrices and Systems of Equations

A group of students decides to sell pizzas to help raise money for their senior class trip. They sold pepperoni for $12, sausage for $10, and cheese for $8. At the end of their sales the class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up a system of three equatio

Square Matrix with Determinant Equal to 0 and Basis for a Solution Space

1) Let A be a square matrix with determinant equal to 0. Prove that if X is a solution to the equation Ax=b then every solution to this equation must have the form x=X+xot where xo is a solution of Ax=0. 2) Find a basis for the solution space of the following system of equations. x- 2x2+ x3 =-4 -2x +3x2 + x4=6 3x -

Gaussian Elimination

Matrices are the most common and popular way to solve systems of equations. Provide an example of a matrix that can be solved using Gaussian elimination. 1. Show specifically how row operations can be used to solve the matrix. 2. State the solution 3. substitute the solution back into the equation to verify the solution.

Matrix Reflection and Rotation Problems

Given the 2x2 matrices A, B, and C (active transformation matrices) in the x, y plane do the following: (A, B and C are 2x2 matrices given below) 1. Show the matrix is orthogonal 2. Find the determinant to indicate if a rotation or reflection matrix 3. Find the rotation angle or find the line of reflection. A= 1/(2)

Matrices with no solutions and infinite solutions

Provide an example of a matrix that has no solution. Use row operations to show why it has no unique solution. Also, some matrices have more than one solution (in fact, an infinite number of solutions) because the system is undetermined. (In other words, there are not enough constraints to provide a unique solution.) Provide an

Use matrix to represent the weight and length

Animal Growth - At the beginning of a laboratory experiment, five baby rats measured. 5.6,6.4,6.9,7.6, and 6.1cm in length, and weighed 144, 138, 149, 152 and 146g, respectively. a). Write a 2*5 matrix using this information b). At the end of two weeks, their lengths ( in centimeters) were 10.2, 11.4, 11.4, 12.7, and 10.8 and

Question about Ordered Pairs

Let A = {a, b, c) and R be the relation defined on A defined by the following matrix: M_R = (1 0 1) (1 1 0) (0 1 1) Describe R by listing the ordered pairs in R and draw the digraph of this relation.

Matrices, Sets and Relations

Let: D = days of the week {M, T, W, R, F}, E = {Brian (B), Jim (J), Karen (K)} be the employees of a tutoring center at a University U = {Courses the tutoring center needs tutors for} = {Calculus I (I), Calculus II (II), Calculus III (III), Computers I (C1), Computers II (C2), Precalculus (P)}. We define the relation R

Row Equivalent Matrices and Systems of Equations

Determine the solutions of the system of equations whose matrix is row-equivalent to: Give three examples of the solutions. Verify that your solutions satisfy the original system of equations.