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Matrices

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

Matrices and Solving Systems of Equations

Please see the attached file for the fully formatted problems. MTH212 Unit 3 - Individual Project B 1. Five neighborhoods (NB) all want to raise money for a playground for their kids. The neighborhood that raises the most money will be able to choose the name of the park. To raise money, they all decide to have a bake sale

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

Together and Alone Problem: Solve by Matrix Methods

Four friends (Gauss, Euler, Cramer, and Einstein) can solve a 20 variable system in 11 hours. Gauss, Euler and Cramer can do it in 18 hours, while Euler, Cramer and Einstein take 16 hours. Gauss, Euler and Einstein can do it together in 14 hours. Define variables, set up a system, and using matrices, determine how long it takes

Matrix Determinants, Transposes and Inverses

If A and B are 3X3 matrices with Det(a)=2 and Det(b)=3 ... if possible evaluate the following expressions 1 Det(2AB) 2 Det(A^4 B^T a^-1) Where T is transpose and -1 is INVERSE

Coordinate Vectors, Transition Matrix and Basis

Let S= { (1, 2), (0, 1)} and T= { (1, 1), (2,3) } be bases for R^2 Let the Vector V=(1,5) and the vector W=(5,4) A. What are the coordinate vectors of V and W wrt to the basis T B. What is the transition matrix P from T to S basis? C. What are the coordinate vectors of V and W wrt to S (Using P from T to S basis)

Matlab : Inverse Operations

With given Eigenvalues λ = 6, -2, 2, 1, - 7 and with given Eigenvectors 5 * 5 matrix given below respectively 1 0 1 2 -1 2 2 1 0 2 3 0 1 2 -3 4 3 1 0 4 5 1 1 3 -5 1) Find inverse power method on (A-1) 2) Shifted inverse power method on (A - CI)-1 Write Matlab script on both the methods.

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

Matrices: Systems of Equations and Determinants

1. Solve the system of equations by using inverse matrix methods: 5x - y = 1 3x + y = 0 2. Find the determinant of matrix (should be brackets) -53 -96 9 2 Please see the attached file for the fully formatted problems.

Similar Transposes

Let N be an kxk matrix such that N^k=0 and N^(k-1) not equal to zero. Show that N and its transpose (N^t) are similar.

Projection matrix

Find a matrix of projection pi onto subspace V parallel to subspace W in R3. See attached file for full problem description.

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.

Matrix Questions

1.(a) If A is invertible and AB = AC, prove that B = C. (b) Let A =24 1 1 1 135 explain why A is not invertible. (c) Let A =24 1 1 1 135, ¯nd 2 matrices B and C, B 6= C such that AB = AC. 2. (a) If a square matrix A has the property that row 1 + row 2 = row 3, clearly explain why the matrix A is not invertible. (b)

Matrix Dimensions and Matrix Division

See attached file for full problem description. Question #2 Only. 2. (a) Find the dimensions of matrix B. Clearly explain your answer. (b) Find matrix B.

Scalar Multiplication of Matrices

For what value of k does equality hold l 5 2 3 l l 1 2 3 l and l 1 2 4 l l 1 2 4 l l -10 3 4 l =k l -2 3 4 l ? l 3 6 9 l =k l 3 6 9 l l-15 4 5 l l -3 4 5 l l 0 5 0 l

Matrices

Find the two numbers whose sum is 76 and quotient is 18. Evaluate the determinate l 8 0 0 l l -16 7 8 l l 8 4 5 l FInd A-1(power) where A = l 2 4 l l 2 5 l