A8.2 Let A be an m × n matrix and B be an n × p matrix. (a) Show that col(B) C null(A) if and onl...

Question

Question

A8.2 Let A be an m × n matrix and B be an n × p matrix. (a) Show that col(B) C null(A) if and only if AB = 0. (b) Show that i

math Advanced-Math

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Ansven that let be mxn matix and e nxp let ie col (B Then is of nx ide and because ne e al column of e all Suc h because hui hen each column of BiGîn nuli Space Hence Thie mplies thal ank (B dim o1 (e) ) s dim (na n) Hence Proved

Add a comment

Answer 2

Similar Homework Help Questions

Let A be an m x n matrix and let B be an n x p...

Let A be an m x n matrix and let B be an n x p matrix. (a) Prove that Col(AB) SColA) (b) Use part (a) to prove that the rank of AB is at most the rank of A (c) Use transpose matrices to prove that the rank of AB is also at most the rank of B.
Let A be an m x 7 matrix of rank r such that Null(A) is a...

Let A be an m x 7 matrix of rank r such that Null(A) is a plane, and Ax = b is always consistent. Then the rank r of A is The nullity of A The dimension of Col(A)) is m = Let T(v) = Av. Is T one-to-one? Is T onto? T: RP → R9, where p = and q = 5 2 5 5 No Yes 7 5 No Yes 3 2 0 1 Cannot be determined. Cannot...
[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be an orthogonal matrix such the PAP...

[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be an orthogonal matrix such the PAP-D,where D is a diagonal matrix with the characteristic roots of A on the diagonal. Show that PA P is also a diagonal matrix. (b) Let A be an m × n matrix of rank m such that A = BC where B and C each has rank m. Show that (BC) CB. 16 STA4801/101/0/2019 (c) For the matrix...

2. * Let A be an m xn matrix, let Col(A) be the column space of...

2. * Let A be an m xn matrix, let Col(A) be the column space of A, and let Nul(A) be the null space of A. (a) Show that Nul(A) is a subspace of R". (b) Show that Col(A) is a subspace of RM
[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be...

[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be an orthogonal matrix such the PAP-D,where D is a diagonal matrix with the characteristic roots of A on the diagonal. Show that PA P is also a diagonal matrix. (b) Let A be an m × n matrix of rank m such that A = BC where B and C each has rank m. Show that (BC) CB. 16 STA4801/101/0/2019 (c) For the matrix...
Please do only e and f and show work null(AT) null(A) T col(A) row(A) Figure 5.6 The four fundamental subspaces (f) Fin...

Please do only e and f and show work null(AT) null(A) T col(A) row(A) Figure 5.6 The four fundamental subspaces (f) Find bases for the four fundamental subspaces of 1 1 1 6 -1 0 1 -1 2 A= -2 3 1 -2 1 4 1 6 1 3 8. Given a subspace W of R", define the orthogonal complement of W to be W vE R u v 0 for every u E W (a) Let W span(e, e2)...

Let A be an mx n matrix and B be an n xp matrix. (a) Prove...

Let A be an mx n matrix and B be an n xp matrix. (a) Prove that rank(AB) S rank(A). (b) Prove that rank(AB) < rank(B).
Let A be an n x p matrix with n p. (a) Show that r(AA) = r(A). (b) Show that I - A(ATA) AT is idempotent. (c) Show that r(1-A(ATAYA") = n-r(A) Let A be an n x p matrix with n p. (a) Show tha...

Let A be an n x p matrix with n p. (a) Show that r(AA) = r(A). (b) Show that I - A(ATA) AT is idempotent. (c) Show that r(1-A(ATAYA") = n-r(A) Let A be an n x p matrix with n p. (a) Show that r(AA) = r(A). (b) Show that I - A(ATA) AT is idempotent. (c) Show that r(1-A(ATAYA") = n-r(A)
Let A be an m x n matrix. Prove that the null-space of AT A, Null...

Let A be an m x n matrix. Prove that the null-space of AT A, Null (AT A), is a subspace of Rn.

Recall that if A is an m times n matrix and B is a p × q matrix

Recall that if A is an m times n matrix and B is a p × q matrix, then the product C = AB is defined if and only if n = p. in which case C is an m × q matrix. a. Write a function M-file that takes as input two matrices A and B, and as output produces the product by rows of the two matrices. For instance, if A is 3 times 4 and B is...

A8.2 Let A be an m × n matrix and B be an n × p matrix. (a) Show that col(B) C null(A) if and onl...

Homework Answers

Add Answer to:
A8.2 Let A be an m × n matrix and B be an n × p matrix. (a) Show that col(B) C null(A) if and onl...

Post as a guest

Earn Coins

Let A be an m x n matrix and let B be an n x p...

Let A be an m x 7 matrix of rank r such that Null(A) is a...

[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be an orthogonal matrix such the PAP...

2. * Let A be an m xn matrix, let Col(A) be the column space of...

[12] QUESTION 4 (a) Let A be an m × m symmetric matrix and P be...

Please do only e and f and show work null(AT) null(A) T col(A) row(A) Figure 5.6 The four fundamental subspaces (f) Fin...

Let A be an mx n matrix and B be an n xp matrix. (a) Prove...

Let A be an n x p matrix with n p. (a) Show that r(AA) = r(A). (b) Show that I - A(ATA) AT is idempotent. (c) Show that r(1-A(ATAYA") = n-r(A) Let A be an n x p matrix with n p. (a) Show tha...

Let A be an m x n matrix. Prove that the null-space of AT A, Null...

Recall that if A is an m times n matrix and B is a p × q matrix

A8.2 Let A be an m × n matrix and B be an n × p matrix. (a) Show that col(B) C null(A) if and onl...

Homework Answers

Add Answer to: A8.2 Let A be an m × n matrix and B be an n × p matrix. (a) Show that col(B) C null(A) if and onl...

Post as a guest

Earn Coins

Add Answer to:
A8.2 Let A be an m × n matrix and B be an n × p matrix. (a) Show that col(B) C null(A) if and onl...