Problem. Let A = [u v w] be a 2 × 3 matrix of rank 1 and suppose u ‡ 0.Show that there is a vector z € R³ such that A = uzT. [Hint: explain why {u}is a basis for the column space of A. What does this say about the relationshipbetween v and u and between w and u?]

As A has rank 1, it's row rank = column rank = 1. So, it's column space is of dimension 1 (i.e.…

Answered: Problem. Let A = [u v w] be a 2 x 3…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(c) Know what it means for a vector u to be in span {x, y}. (d) Given an m x n matrix A, know definition of Null A, Im A and how to find them. (e) Given a matrix A, and a vector v, determine whether v is in Null A, in Im A.
Determine whether the vector u belongs to the null space of the matrix A. --14-638 U= , A = -1 -3 11
3. Find an example of a matrix that has Why can't this be a basis for the row space and the mullspace? 1. Explain why the vector v = H and as a basis for its row space and its column space. cannot be a row of A and also in the nullspace of A.
Let a₁,..., a5 denote the columns of the matrix A, where 5 1 2 2 0 332 -1 84 4 −5 -2 1 1 0 -12 12 -2 A = B = [a₁ a₂ a4] Explain why a3 and a5 are in the column space of B. Find a set of vectors that spans the null space of A, N(A). Determine the dimensions of N(A), col(A), R(A) for the matrix A.
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. 0 --[142-9] A = -5 A nonzero vector in Nul A is (Type an integer or decimal for each matrix element.) A nonzero vector in Col A is. (Type an integer or decimal for each matrix element.)
1. Let a(x, y) represent the area of the parallelogram formed by the 2-dimensional vectors x and y. Prove that if u and v are two 2-dimensional vectors and A is a 2 x 2 matrix, then a(Au, Av) = det(A)a(u, v).

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Problem. Let A = [u v w] be a 2 x 3 matrix of rank 1 and suppose u + 0. Show that there is a vector z € R³ such that A = uzT. [Hint: explain why {u} is a basis for the column space of A. What does this say about the relationship between v and u and between w and u?]