Question 1

Convert the augmented matrix to the equivalent linear system.

Accepted Answer

The answer of Convert the augmented matrix to the equivalent...

Question 2

Convert the given system to an augmented matrix, and find all solutions by reducing to echelon form and using back substitution.

Accepted Answer

The answer of Convert the given system to an augmented...

Question 3

Determine which of the points (2, -3), (2, 3), and (4, 2) lie on both of the lines 
   and 
   
.

Accepted Answer

(2, 3)

Question 4

Use a system of linear equations to find the values 
   and 
   for the partial fraction decomposition

Accepted Answer

The answer of Use a system of linear equations to...

Question 5

An economy has three industries: A, B, and C. These industries have annual consumer sales of 45, 37, and 64 (in millions of dollars), respectively. In addition, for every dollar of goods that A sells, A requires 25 cents from B and 15 cents from C. For each dollar of goods that B sells, B requires 35 cents from A and 25 cents from C. For each dollar of goods that C sells, C requires 20 cents from A and 45 cents from B. Let a, b, c be the total output from industries A, B, C, respectively. What values of a, b, c (rounded to the nearest thousand dollars) will satisfy both consumer and between-industry demand?

Accepted Answer

a = $105,764,000; b

Question 6

A linear system with a unique solution can not have more variables than equations.

Accepted Answer

A) True 
 B)False

Question 7

Compute the first three Gauss-Seidel iterations for the system in question 6, using 
   as the initial value for each variable. Then find the exact solution and compare.

Accepted Answer

@#IMG-DLM& 
 Exact s

Question 8

Convert the augmented matrix to the equivalent linear system.

Accepted Answer

The answer of Convert the augmented matrix to the equivalent...

Question 9

Determine which of (3, s2, s1, 2), (0, 0, 0 ,0), (2 - s1 - s2, 1 + s1 + s2, s1, s2), and (3 - s1, s1, s2, 2 - s2) form a solution to the following system for all choices of the free parameters 
   
.

Accepted Answer

(2 - s₁ - s

Question 10

If a linear system has more variables than equations, then the system is inconsistent.

Accepted Answer

A) True 
 B)False

Question 11

Solve the given system using Gaussian elimination with three significant digits of accuracy. Then solve the system again, incorporating partial pivoting.

Accepted Answer

Gaussian elimination

Question 12

Compute the first four Jacobi iterations for the system as written, with the initial value of each variable set equal to 
   
. Then rewrite the system so that it is diagonally dominant, set the value of each variable to 0, and again compute four Jacobi iterations. Finally, find the exact solution and compare.

Accepted Answer

Jacobi iteration:

Question 13

Compute the first four Jacobi iterations for the system as written, with the initial value of each variable set equal to 
   
. Then rewrite the system so that it is diagonally dominant, set the value of each variable to 0, and again compute four Jacobi iterations. Finally, find the exact solution and compare.

Accepted Answer

Jacobi iteration:

Question 14

Use a system of linear equations to find a function of the form 
   such that 
   
, 
   
, 
   
, and 
   
.

Accepted Answer

The answer of Use a system of linear equations to...

Question 15

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Accepted Answer

Echelon form; leadin

Question 16

Compute the first four Gauss-Seidel iterations for the system in question 10, with the initial value of each variable set equal to 0. Then rewrite the system so that it is diagonally dominant, set the value of each variable to 0, and again compute four Gauss-Seidel iterations.

Accepted Answer

Gauss-Seidel iterati

Question 17

Find all solutions to the system

Accepted Answer

The answer of Find all solutions to the system
 ...

Question 18

Every homogeneous linear system has at least one solution.

Accepted Answer

A) True 
 B)False

Question 19

Balance the given chemical equation.

Accepted Answer

The answer of Balance the given chemical equation.
  ...

Question 20

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Accepted Answer

Reduced ec

Convert the augmented matrix to the equivalent linear system.

Convert the given system to an augmented matrix, and find all solutions by reducing to echelon form and using back substitution.

Determine which of the points (2, -3), (2, 3), and (4, 2) lie on both of the lines and .

A linear system with a unique solution can not have more variables than equations.

Compute the first three Gauss-Seidel iterations for the system in question 6, using as the initial value for each variable. Then find the exact solution and compare.

Convert the augmented matrix to the equivalent linear system.

Determine which of (3, s₂, s₁, 2), (0, 0, 0 ,0), (2 - s₁ - s₂, 1 + s₁ + s₂, s₁, s₂), and (3 - s₁, s₁, s₂, 2 - s₂) form a solution to the following system for all choices of the free parameters .

If a linear system has more variables than equations, then the system is inconsistent.

Solve the given system using Gaussian elimination with three significant digits of accuracy. Then solve the system again, incorporating partial pivoting.

Use a system of linear equations to find a function of the form such that , , , and .

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Compute the first four Gauss-Seidel iterations for the system in question 10, with the initial value of each variable set equal to 0. Then rewrite the system so that it is diagonally dominant, set the value of each variable to 0, and again compute four Gauss-Seidel iterations.

Find all solutions to the system

Every homogeneous linear system has at least one solution.

Balance the given chemical equation.

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Euclidean Space

Matrices

Subspaces

Determinants

Eigenvalues and Eigenvectors

Vector Spaces

Orthogonality

Linear Transformations

Inner Product Spaces

Additional Topics and Applications

Filters

Exam 1: Systems of Linear Equations

Convert the augmented matrix to the equivalent linear system.

Convert the given system to an augmented matrix, and find all solutions by reducing to echelon form and using back substitution.

Determine which of the points (2, -3), (2, 3), and (4, 2) lie on both of the lines and .

Use a system of linear equations to find the values and for the partial fraction decomposition

A linear system with a unique solution can not have more variables than equations.

Compute the first three Gauss-Seidel iterations for the system in question 6, using as the initial value for each variable. Then find the exact solution and compare.

Convert the augmented matrix to the equivalent linear system.

Determine which of (3, s2, s1, 2), (0, 0, 0 ,0), (2 - s1 - s2, 1 + s1 + s2, s1, s2), and (3 - s1, s1, s2, 2 - s2) form a solution to the following system for all choices of the free parameters .

If a linear system has more variables than equations, then the system is inconsistent.

Solve the given system using Gaussian elimination with three significant digits of accuracy. Then solve the system again, incorporating partial pivoting.

Use a system of linear equations to find a function of the form such that , , , and .

Determine if the system is in echelon form, and if so, identify the leading variables and the free variables. If it is not in echelon form, explain why.

Compute the first four Gauss-Seidel iterations for the system in question 10, with the initial value of each variable set equal to 0. Then rewrite the system so that it is diagonally dominant, set the value of each variable to 0, and again compute four Gauss-Seidel iterations.

Find all solutions to the system

Every homogeneous linear system has at least one solution.

Balance the given chemical equation.

Determine whether the matrix is in reduced echelon form, echelon form only, or not in echelon form.

Euclidean Space

Matrices

Subspaces

Determinants

Eigenvalues and Eigenvectors

Vector Spaces

Orthogonality

Linear Transformations

Inner Product Spaces

Additional Topics and Applications

Filters

Determine which of (3, s₂, s₁, 2), (0, 0, 0 ,0), (2 - s₁ - s₂, 1 + s₁ + s₂, s₁, s₂), and (3 - s₁, s₁, s₂, 2 - s₂) form a solution to the following system for all choices of the free parameters .