say we have a matrix like this with an all zero row at the bottom. Why is it that we will have infinitely many solutions? also if the constant in the last row was a not zero then there would be no solutions right?
thanks for the help
Homework Answers
In a matrix the number of rows is equal to the number of variables in the system of equation.
If the matrix has all zero errors at the bottom then it means one the variable is free which means that free variable can take Infinitely many values hence it has Infinitely many solution.
If the constant in the last row is not zero then it has no solution because in that case
0x+0y+0z =6
Where 6 is that constant which is not zero in the last row
Therefore solving we get 0=6
Which is not possible, hence no solution
Add Answer to:
say we have a matrix like this with an all zero row at
the bottom. Why...
(ii) Our swapped system now looks like: -6x+3y7 3 2y 3 Let's say you now wanted...
(ii) Our swapped system now looks like: -6x+3y7 3 2y 3 Let's say you now wanted to solve this new swapped system of equations by multiplying the bottom equation by 2 and adding it to the top equation to eliminate the r to solve for y. We can do this in the matrix equation as well. Rewrite the swapped matrix equation so that it represents what happens when you take 2 times the bottom equation, add it to the top...
Problem 2 We have seen that, if a matrix A is invertible, then we can express...
Problem 2 We have seen that, if a matrix A is invertible, then we can express the unique solution of Az = b as I = A-15. Soon, we will introduce ideas that help us understand At = b better when A is not invertible. This problem is preparation for that! 11 301 1-3 -9 2 Let A = 2 6 0 1-2 -6 -5 (a) Solve the system A7 = 5. (b) What does the solution set of Az...
We say that an nxn matrix is skew-symmetric if A^T=-A. Let W be the set of...
We say that an nxn matrix is skew-symmetric if A^T=-A. Let W be
the set of all 2x2 skew-symmetric matrices: W = {A in m2x2(R) l
A^T=-A}.
(a) Show that W is a subspace of M2x2(R)
(b) Find a basis for W and determine dim(W).
(c) Suppose T: M2x2(R) is a linear transformation given by
T(A)=A^T +A. Is T injective? Is T surjective? Why or why not? You
do not need to verify that T is linear.
3. (17 points)...
could you please help me with understanding why the answer to d) is not 3 parameters but instead 5,4 or 3? In a row...
could you please help me with understanding why the answer to
d) is not 3 parameters but instead 5,4 or 3? In a row echelon form,
don’t we know that each non-zero rows has a leading 1 (by
definition)? And so we know that the rank must be 3? 6-3=3 (by
given theorem: n-r= #parameter)
4xy + 5ax2- 2ay +5x4 + 2xs 2x4+2xs 4x4 +x = 0 in ce 2x3- 9. (a) 2x, +2x- 4a x a + 2ax3 +...
Could anyone help me with this math problem please.. 1. Recall that a system of linear...
Could anyone help me with this math problem please..
1. Recall that a system of linear equations is singular if it has none or infinitely many solutions. Explain why the system u+2w = 0 is singular by finding a combination of the three equations that adds up to 0 = 1. What value should replace the last zero on the right side to allow the equations to have solutions-and what is one of the solutions?
need help a) For the system of equations given, partially row reduce the coefficient matrix in...
need help
a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2yı - 24 = 5 4x1 +9yı - 321 = 8 (5x, +12yı - 324 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to l's). Reduce from left to right through the columns and from the pivot entry down...
MPORTANT: If you are going to write please make sure your writing is neat, legible, and...
MPORTANT: If you are going to write please make sure your
writing is neat, legible, and easy to read. Please write in print
(not cursive). Thank you
IMPORTANT: I know the answer is given bellow, but I do have a
couple of conceptual things I'd like explained. I know it may be a
bit silly, but please explain to me what it means for a matrix to
be "linearly independent" and why the matrix (in this case) is not
linearly...
Please show all steps in completing this problem, thank you very much! Solve the system Ax=b...
Please show all steps in completing this problem, thank
you very much!
Solve the system Ax=b using the LU factorization of A and the matrix b given below. -2 0 0 1 -1 -2 7 A=LU= -2 -1 0 0 1 3 -17 2 -1 -2 0 0 1 -5 b= 12 12 -10 You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. The system has infinitely many solutions Number of Parameters:...
Please highlight answers and answer all questions in each question The reduced row echelon form of...
Please highlight answers and answer all questions in each
question
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x and y as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution 10 -5 0 1 8 What equation does the first row represent? x= -5 (Type an equation.) What equation does the second row represent? y =...
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if...
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if false what would make it true, or a counterexample - 2 pts each: a. If Spanv v, V}) = Span({w,W)= W , then W is 2-dimensional. b. The kernel of a linear transformation T: R8 -R5 cannot be trivial c. If A is an invertible matrix, then A is diagonalizable 0, then A cannot be full-rank d. If det(A) e. If A is an...
(ii) Our swapped system now looks like: -6x+3y7 3 2y 3 Let's say you now wanted to solve this new swapped system of equations by multiplying the bottom equation by 2 and adding it to the top equation to eliminate the r to solve for y. We can do this in the matrix equation as well. Rewrite the swapped matrix equation so that it represents what happens when you take 2 times the bottom equation, add it to the top...
Problem 2 We have seen that, if a matrix A is invertible, then we can express the unique solution of Az = b as I = A-15. Soon, we will introduce ideas that help us understand At = b better when A is not invertible. This problem is preparation for that! 11 301 1-3 -9 2 Let A = 2 6 0 1-2 -6 -5 (a) Solve the system A7 = 5. (b) What does the solution set of Az...
We say that an nxn matrix is skew-symmetric if A^T=-A. Let W be
the set of all 2x2 skew-symmetric matrices: W = {A in m2x2(R) l
A^T=-A}.
(a) Show that W is a subspace of M2x2(R)
(b) Find a basis for W and determine dim(W).
(c) Suppose T: M2x2(R) is a linear transformation given by
T(A)=A^T +A. Is T injective? Is T surjective? Why or why not? You
do not need to verify that T is linear.
3. (17 points)...
could you please help me with understanding why the answer to
d) is not 3 parameters but instead 5,4 or 3? In a row echelon form,
don’t we know that each non-zero rows has a leading 1 (by
definition)? And so we know that the rank must be 3? 6-3=3 (by
given theorem: n-r= #parameter)
4xy + 5ax2- 2ay +5x4 + 2xs 2x4+2xs 4x4 +x = 0 in ce 2x3- 9. (a) 2x, +2x- 4a x a + 2ax3 +...
Could anyone help me with this math problem please..
1. Recall that a system of linear equations is singular if it has none or infinitely many solutions. Explain why the system u+2w = 0 is singular by finding a combination of the three equations that adds up to 0 = 1. What value should replace the last zero on the right side to allow the equations to have solutions-and what is one of the solutions?
need help
a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: *1 + 2yı - 24 = 5 4x1 +9yı - 321 = 8 (5x, +12yı - 324 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to l's). Reduce from left to right through the columns and from the pivot entry down...
MPORTANT: If you are going to write please make sure your
writing is neat, legible, and easy to read. Please write in print
(not cursive). Thank you
IMPORTANT: I know the answer is given bellow, but I do have a
couple of conceptual things I'd like explained. I know it may be a
bit silly, but please explain to me what it means for a matrix to
be "linearly independent" and why the matrix (in this case) is not
linearly...
Please show all steps in completing this problem, thank
you very much!
Solve the system Ax=b using the LU factorization of A and the matrix b given below. -2 0 0 1 -1 -2 7 A=LU= -2 -1 0 0 1 3 -17 2 -1 -2 0 0 1 -5 b= 12 12 -10 You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. The system has infinitely many solutions Number of Parameters:...
Please highlight answers and answer all questions in each
question
The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x and y as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution 10 -5 0 1 8 What equation does the first row represent? x= -5 (Type an equation.) What equation does the second row represent? y =...
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if false what would make it true, or a counterexample - 2 pts each: a. If Spanv v, V}) = Span({w,W)= W , then W is 2-dimensional. b. The kernel of a linear transformation T: R8 -R5 cannot be trivial c. If A is an invertible matrix, then A is diagonalizable 0, then A cannot be full-rank d. If det(A) e. If A is an...
Most questions answered within 3 hours.
-
How can we identify what the horizontal force is when looking at
a merry go round?...
asked 7 minutes ago -
While Dime Community Bank is based in Brooklyn; management has
decided to focus its lending activity...
asked 32 minutes ago -
1) Earnings functions, whereby the log of earnings is regressed
on years of education, years of...
asked 6 minutes ago -
Bruno Corporation is involved in the business of injection
molding of plastics. It is considering the...
asked 11 minutes ago -
What would be the vapor pressure of water at 96°C above a
solution made by dissolving...
asked 26 minutes ago -
Hydration of norbornene
Write the reaction. Discuss the intermediate. Explain how the
equilibrium in the reaction...
asked 33 minutes ago -
Suppose that a party wanted to enter an FRA that expires in 42
days and is...
asked 34 minutes ago -
ABC Ltd. estimated that a new store requires an initial
investment of $800,000. This new store...
asked 34 minutes ago -
1. Review the Nike’s marketing strategy. You must include the
company’s target market, possible market segmentation,...
asked 47 minutes ago -
One of the major advantages of ______________ is to enhance
security for private networks by keeping...
asked 53 minutes ago -
Book:
Title: Framework for
Marketing Management, 15th edition
Author/s: Philip T.
Kotler, Kevin Lane Keller
1....
asked 1 hour ago -
Given Uber’s recent corporate turbulence and ongoing
initiatives, provide a holistic situational analysis of the
environment...
asked 1 hour ago