Consider the following matrix A: 3-3-3 3-1-7 A = 2-3 3 2 -3 -2 For each of the following vectors, determine whether the vector is in the column space of A. If so, demonstrate this by providing a vector x so that Ax-b₁. b₁ = b3 = -6 -18 8 -2 3 15 -10 0 ܬ 5 -3 6 b₁ is in col(a): 0 A0 =b₁ 0 b2 is in col(a): 0 A0=b₂ b3 is in col(a): A0 =b3

Consider the following matrix A: 3-3-3 3-1-7 A = 2-3 3 2 -3 -2 For each of the following vectors, determine whether the vector is in the column space of A. If so, demonstrate this by providing a vector x so that Ax-b₁. b₁ = b3 = -6 -18 8 -2 3 15 -10 0 ܬ 5 -3 6 b₁ is in col(a): 0 A0 =b₁ 0 b2 is in col(a): 0 A0=b₂ b3 is in col(a): A0 =b3

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...

See similar textbooks

Similar questions

Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of B and the column vectors of AB are in the column space of A.
Find two nonzero matrices A and B such that AB=BA.
Draw the following vectors in standard position in 2 : aa=30bb=23cc=23dd=32