Question

Is the span of the rows of a matrix the same as the span of the...

Is the span of the rows of a matrix the same as the span of the rows of its rref form?

If the nullity of a matrix A is 0, is the system Ax=y always consistent regardless of what y?

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

Homework Answers

Answer #1

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
True/ false a- If the last row in an REF of an augmented matrix is [0...
True/ false a- If the last row in an REF of an augmented matrix is [0 0 0 4 0], then the associated linear system is inconsistent. b-The equation Ax=b is consistent if the augmented matrix [A b] has a pivot position in every row. c-The set Span{v} for a nonzero v is always a line that may or may not pass through the origin.
True or False (5). Suppose the matrix A and B are both invertible, then (A +...
True or False (5). Suppose the matrix A and B are both invertible, then (A + B)−1 = A−1 + B−1 . (6). The linear system ATAx = ATb is always consistent for any A ∈ Rm×n, b ∈Rm . (7). For any matrix A ∈Rm×n , it satisfies dim(Nul(A)) = n−rank(A). (8). The two linear systems Ax = 0 and ATAx = 0 have the same solution set. (9). Suppose Q ∈Rn×n is an orthogonal matrix, then the row...
. Given vectors v1, ..., vk in F n , by reducing the matrix M with...
. Given vectors v1, ..., vk in F n , by reducing the matrix M with v1, ..., vk as its rows to its reduced row echelon form M˜ , we can get a basis B of Span ({v1, ..., vk}) consisting of the nonzero rows of M˜ . In general, the vectors in B are not in {v1, ..., vk}. In order to find a basis of Span ({v1, ..., vk}) from inside the original spanning set {v1, ...,...
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...
Here are some vectors in R 4 : u1 = [1 3 −1 1] u2 =...
Here are some vectors in R 4 : u1 = [1 3 −1 1] u2 = [1 4 −1 1] u3 = [1 0 −1 1] u4 = [2 −1 −2 2] u5 = [1 4 0 1] (a) Explain why these vectors cannot possibly be independent. (b) Form a matrix A whose columns are the ui’s and compute the rref(A). (c) Solve the homogeneous system Ax = 0 in parametric form and then in vector form. (Be sure the...
1. Let a,b,c,d be row vectors and form the matrix A whose rows are a,b,c,d. If...
1. Let a,b,c,d be row vectors and form the matrix A whose rows are a,b,c,d. If by a sequence of row operations applied to A we reach a matrix whose last row is 0 (all entries are 0) then:        a. a,b,c,d are linearly dependent   b. one of a,b,c,d must be 0.       c. {a,b,c,d} is linearly independent.       d. {a,b,c,d} is a basis. 2. Suppose a, b, c, d are vectors in R4 . Then they form a...
4. Suppose that we have a linear system given in matrix form as Ax = b,...
4. Suppose that we have a linear system given in matrix form as Ax = b, where A is an m×n matrix, b is an m×1 column vector, and x is an n×1 column vector. Suppose also that the n × 1 vector u is a solution to this linear system. Answer parts a. and b. below. a. Suppose that the n × 1 vector h is a solution to the homogeneous linear system Ax=0. Showthenthatthevectory=u+hisasolutiontoAx=b. b. Now, suppose that...
Write the system of equations as an augmented matrix. Then solve the system by putting the...
Write the system of equations as an augmented matrix. Then solve the system by putting the matrix in reduced row echelon form. x+2y−z=-10 2x−3y+2z=2 x+y+3z=0
Suppose ⃗v1,⃗v2,⃗v3,⃗v4 ∈ R3. Let V = {⃗v1,⃗v2,⃗v3,⃗v4} and let X = [⃗v1|⃗v2|⃗v3|⃗v4] be the matrix...
Suppose ⃗v1,⃗v2,⃗v3,⃗v4 ∈ R3. Let V = {⃗v1,⃗v2,⃗v3,⃗v4} and let X = [⃗v1|⃗v2|⃗v3|⃗v4] be the matrix whose columns are ⃗v1,⃗v2,⃗v3,⃗v4. Suppose further that every subset Y ⊂ V of size two is linearly independent. Explain what form(s) rref(X), the reduced row echelon form of X, must take in this case. Hint: you won’t be able to pin down exact numbers for every entry of rref(X), but you might know things like whether the entry can be zero or not, etc.
a)Assume that you are given a matrix A = [aij ] ∈ R n×n with (1...
a)Assume that you are given a matrix A = [aij ] ∈ R n×n with (1 ≤ i, j ≤ n) and having the following interesting property: ai1 + ai2 + ..... + ain = 0 for each i = 1, 2, ...., n Based on this information, prove that rank(A) < n. b) Let A ∈ R m×n be a matrix of rank r. Suppose there are right hand sides b for which Ax = b has no solution,...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT