3 (b) Write the following systems of linear equations as matrix equation and then as an augmented matrix:
(4marks)
(d) Use Cramer’s rule to solve the system of 2 linear equations in 3(b). (7marks)
Homework Answers
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3 (b) Write the following systems of linear equations as matrix
equation and then as an...
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y=...
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1
Consider the following non-homogeneous system of differential equations. a. Write the system in matrix form. b....
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
(5) Let b = and let A be the matrix . Is b in the range...
(5)
Let b = and let A be the
matrix . Is b in the
range of the linear transformation
x↦Ax? Why or why not?
We were unable to transcribe this imageWe were unable to transcribe this imageLet b= 1 -3 5 -51 1, and let A be the matrix O 1 -3 5 . Is b in the range of the linear transformation x 2 - 4 4 - 4 Ax? Why or why not? Is b in the...
1. For each of the following systems of linear equations, find: • the augmented matrix •...
1. For each of the following systems of linear equations, find: • the augmented matrix • the coefficient matrix • the reduced row echelon form of the augmented matrix • the rank of the augmented matrix • all solutions to the original system of equations Show your work, and use Gauss-Jordan elimination (row reduction) when finding the reduced row echelon forms. (b) 2 + 2x W 2w - 2y - y + y + 3z = 0 = 1 +...
Linear Algebra: Systems of Linear Differential Equations and Eigenvalues Solve the system: Also, Show the work...
Linear Algebra: Systems of Linear Differential Equations and
Eigenvalues
Solve the system:
Also, Show the work to find the eigenvalues (this is the most
important part for me)
We were unable to transcribe this imagey = 3y1 + 2yz
2. Solve the following linear systems of equations by writing the system as a matrix equation...
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
Write a program in Matlab that solves linear systems of equations using Gauss elimination with pa...
Write a program in Matlab that solves linear systems of
equations using Gauss elimination with partial pivoting. Make sure
that you use variables that are explicit, and make sure to include
comment lines (each subroutine should have at least a sentence
stating what it does). Make sure that your program checks for valid
inputs in matrix and vectors dimensionality.
• Using your code, solve the systems of equations in problems
9.11, 9.12, and 9.13
9.11
9.12
9.13
2x1-6x2-X3 =-38 We...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
a) Write the augmented matrix for the linear system that corresponds to the matrix equation AX...
a) Write the augmented matrix for the linear system that
corresponds to the matrix equation AX = b
b) solve the above system
c) write the solution as a vector
A= 0 4 5 -1 3 2 and b= 1 24 5 4 2
Write the following system of equations in the form AX = B, and calculate the solution...
Write the following system of equations in the form AX = B, and
calculate the solution using the equation
x + y = -6
3x - y = -2
We were unable to transcribe this imageWe were unable to transcribe this image
3. Write the following systems of linear equations using augmented matrix form a. 6x+7y= -9 X-y= 5 b. 2x-5y= 4 4x+3y= 5 C. x+y+z= 4 2x-y-z= 2 -x+2y+3z= 5 4. Solve the following Systems of linear equations using Cramer's Rule a. 6x-3y=-3 8x-4y= -4 b. 2x-5y= -4 4x+3y= 5 c. 2x-3y+z= 5 X+2y+z= -3 x-3y+2z= 1
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
(5)
Let b = and let A be the
matrix . Is b in the
range of the linear transformation
x↦Ax? Why or why not?
We were unable to transcribe this imageWe were unable to transcribe this imageLet b= 1 -3 5 -51 1, and let A be the matrix O 1 -3 5 . Is b in the range of the linear transformation x 2 - 4 4 - 4 Ax? Why or why not? Is b in the...
1. For each of the following systems of linear equations, find: • the augmented matrix • the coefficient matrix • the reduced row echelon form of the augmented matrix • the rank of the augmented matrix • all solutions to the original system of equations Show your work, and use Gauss-Jordan elimination (row reduction) when finding the reduced row echelon forms. (b) 2 + 2x W 2w - 2y - y + y + 3z = 0 = 1 +...
Linear Algebra: Systems of Linear Differential Equations and
Eigenvalues
Solve the system:
Also, Show the work to find the eigenvalues (this is the most
important part for me)
We were unable to transcribe this imagey = 3y1 + 2yz
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
Write a program in Matlab that solves linear systems of
equations using Gauss elimination with partial pivoting. Make sure
that you use variables that are explicit, and make sure to include
comment lines (each subroutine should have at least a sentence
stating what it does). Make sure that your program checks for valid
inputs in matrix and vectors dimensionality.
• Using your code, solve the systems of equations in problems
9.11, 9.12, and 9.13
9.11
9.12
9.13
2x1-6x2-X3 =-38 We...
Given the following system of linear equations 1. 2xi + 4x2 + 8 x3 + x. +2x,3 a) Write the augmented matrix that represents the system b) Find a reduced row echelon form (RREF) matrix that is row equivalent to the augmented matrix c) Find the general solution of the system d) Write the homogeneous system of equations associated with the above (nonhomogeneous) system and find its general solution.
Given the following system of linear equations 1. 2xi + 4x2...
a) Write the augmented matrix for the linear system that
corresponds to the matrix equation AX = b
b) solve the above system
c) write the solution as a vector
A= 0 4 5 -1 3 2 and b= 1 24 5 4 2
Write the following system of equations in the form AX = B, and
calculate the solution using the equation
x + y = -6
3x - y = -2
We were unable to transcribe this imageWe were unable to transcribe this image
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