Question

If the reduced row echelon form of an m*n matrix A has a pivot in every...

If the reduced row echelon form of an m*n matrix A has a pivot in every row, explain why the columns of A must span R^m

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

as A is in reduced row echelon form then there is at least M columns which are linearly independent by using this result i solved this

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
T12. Suppose that A is a square matrix. Using the definition of reduced row-echelon form (Definition...
T12. Suppose that A is a square matrix. Using the definition of reduced row-echelon form (Definition RREF) carefully, give a proof of the following equivalence: Every column of A is a pivot column if and only if A is the identity matrix (Definition IM). http://linear.ups.edu/html/section-NM.html
Solve and explain the process of solving the following system with matrix reduced row-echelon form. Last,...
Solve and explain the process of solving the following system with matrix reduced row-echelon form. Last, explain your results for the following problem: 3x – 4y + 4z =7 x – y – 2z = 2 2x – 3y + 6z = 5
Show that the nonzero rows of a reduced row echelon form A form a basis of...
Show that the nonzero rows of a reduced row echelon form A form a basis of the row space R (A). Hint: Name the positions of pivotal entries by indices of the form (i, ki) with ki+1 > ki .
Recall the methods for finding bases of the row and column space of a matrix A...
Recall the methods for finding bases of the row and column space of a matrix A which were shown in lectures. To find a basis for the row space we row reduce and then take the non zero rows in reduced row echelon form, and to find a basis for the column space we row reduce to find the pivot columns and then take the corresponding columns from the original matrix. In this question we consider what happens if we...
Solve the following systems by forming the augmented matrix and reducing to reduced row echelon form....
Solve the following systems by forming the augmented matrix and reducing to reduced row echelon form. In each case decide whether the system has a unique solution, infinitely many solutions or no solution. Show pivots in squares. Describe the solution set. -3x1+x2-x3=10 x2+4X3=12 -3x1+2x2+3x3=11
The pivot columns of an echelon form of A always form a basis for column A.
The pivot columns of an echelon form of A always form a basis for column A.
Answer all of the questions true or false: 1. a) If one row in an echelon...
Answer all of the questions true or false: 1. a) If one row in an echelon form for an augmented matrix is [0 0 5 0 0] b) A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. c) The solution set of b is the set of all vectors of the form u = + p + vh where vh is any solution...
Consider the following matrix A and its reduced row-echelon form: Find the dimensions of row(A), null(A),...
Consider the following matrix A and its reduced row-echelon form: Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. A= ( < 0, 0, 0,1 > , < 0, 0, 0, 3 >, < 3, 0, -3, -2> , < 6, 0, -6, -9 > , < -3, -5, 13 , -2 >, <-6, -10, 26, -8 > ) rref = ( < 1, 0 ,0, 0 >, < 3, 0, 0, 0...
Find the reduced row echelon form of the following matrices. Interpret your result by giving the...
Find the reduced row echelon form of the following matrices. Interpret your result by giving the solutions of the systems whose augmented matrix is the one given. [ 0 4 7 0 2 1 0 0 0 3 1 -4 ]
Write a Matlab function that will return the row canonical form for any given row echelon...
Write a Matlab function that will return the row canonical form for any given row echelon matrix; your function should return an appropriate error if the input matrix is NOT in echelon form.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT