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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

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.

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)

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

Matrices and Pivot Positions : Solutions for Ax+0 and Ax=b

In problems 1-4 (a) does the equation Ax = 0 have a nontrivial solution and (b) does the equation the Ax = b have at least one solution for every possible b? 1) A is a 3x3 matrix with three pivot positions. 2) A is a 3x3 matrix with two pivot positions. 3) A is a 3x2 matrix with two pivot positions. 4) A is a 2x4 matrix

Matrices & Vectors: Matrix Products, Ax=B and Linear Combination

Please see the attached file for the fully formatted problems. Compute the products using the row vector rule for computing Ax. If a product is undefined, explain why. 1) 2) 3) 4) let A = and b = . Show that the equation Ax=b does not have a solution for all possible b, and describe the set of all b for which Ax=b does

Row Operations and Matrix Dimensions

Please see the attached file for the fully formatted problems. 6. Perform the row operation (-2) R1 + R2  R2 on the matrix . 8. What are the dimensions of the matrices shown below? a) b) 9. Find

Invertible Lower Triangular Matrix, Adjoints and Inverses

Find A^-1 using Theorem 2.1.2 - Inverse of a Matrix Using Its Adjoint: If A is an invertible matrix, then A-1 = [1/det(A)] * [adj(A)] A = 2 0 3 0 3 2 -2 0 -4 Prove that if A is an invertible lower triangular matrix, then A-1 is lower triangular.

Lesson 5631-2: Matrices

43 Matrix Problems. See attached file for full problem description. 1. The symobl [A] denotes a 2. For a mn matrix (m rows and n columns) when m = n, the matrix is said to be 3. The matrix [0 2 3] is a 4. The number of columns in a column matrix is 5. In the matrix [A] = [ 1 6; 5 2; 0 -3], the element a_32 is

Matrices and Systems of Equations Word Problems

The meteorologists at the National Interagency Fire Center had pizza delivered to their operations center. Their lunch consisted of pizza, milk and gelatin. One slice of cheese pizza contains 290 calories, 15g of protein, 9g of fat, and 39g of carbohydrates. One-half cup of gelatin dessert contains 70 calories, 2g of protein, 0g

Matrices and Systems of Equations Word Problems

The meteorologists at the National Interagency Fire Center had pizza delivered to their operations center. Their lunch consisted of pizza, milk and gelatin. One slice of cheese pizza contains 290 calories, 15g of protein, 9g of fat, and 39g of carbohydrates. One-half cup of gelatin dessert contains 70 calories, 2g of protein, 0g