Question

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.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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
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...
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
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 .
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...
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.
why is it that when findinf the basis for a set of vectors you row reduce...
why is it that when findinf the basis for a set of vectors you row reduce the augmented matrix with zero and then find the pivot columns ans the set of correspondingvectors in the original matrix form the basis, however whej youre finding a basis for the eigenspace, and you do A-lambda*I, why dont you do the same procedure with that matrix?
Argue that the only way for a square matrix Ain reduced echelon form Arr to have...
Argue that the only way for a square matrix Ain reduced echelon form Arr to have a non-zero determinant is if Arr=I, the identity matrix.
*When do we use tied columns? What about spiral columns? *How does the behavior of column...
*When do we use tied columns? What about spiral columns? *How does the behavior of column affected by using each type of confinement? (Tied vs Spiral) *What is the behavior of each type when axially and eccentrically loaded (Tied vs Spiral) *How does the eccentricity ratio (e/h) affect the selection of the type of columns (Tied vs Spiral) *What are the other differences of Tied vs Spiral columns
vectors u=(1,2,3), v=(2,5,7), w=(1,3,5) are linearly dependent or independent? (using echelon form)
vectors u=(1,2,3), v=(2,5,7), w=(1,3,5) are linearly dependent or independent? (using echelon form)