Complete parts A-F for matrix A, and vector b given below [3 -9 12 -9 6 15 A = 3 -7 8 -5 8 9,b= 9 0 3 -664-5 (a) Find the reduced row echelon form of the augmented matrix Ax=b by hand and write the solution as a linear combination of vectors. (b) Identify the null space of A? (c) What is the dimension of the null space? (d) Find a matrix, R, with dimensions 6 x 3 such that AR = 0(Note: Matrix R cannot be the 0 matrix.)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 17E
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I'm really just having trouble with part D, since R cant be the zero matrix but we must have zero at the end, does that mean we have to turn it into the identity matrix (im assuming identity is zero?). so then does that mean R needs to be the inverse? im not sure

1. Complete parts A-F for matrix A, and vector b given below
3
A = 3 -7
-9 12 -9 6 15
8 -58 9 ,b= 9
0 3 -6 6 4-5
(a) Find the reduced row echelon form of the augmented matrix Ax=b by hand and write the solution as a
linear combination of vectors.
(b) Identify the null space of A?
(c) What is the dimension of the null space?
(d) Find a matrix, R, with dimensions 6 x 3 such that AR = 0(Note: Matrix R cannot be the 0 matrix.)
(e) What is the column space of A?
(f) What is the dimension of the column space?
Transcribed Image Text:1. Complete parts A-F for matrix A, and vector b given below 3 A = 3 -7 -9 12 -9 6 15 8 -58 9 ,b= 9 0 3 -6 6 4-5 (a) Find the reduced row echelon form of the augmented matrix Ax=b by hand and write the solution as a linear combination of vectors. (b) Identify the null space of A? (c) What is the dimension of the null space? (d) Find a matrix, R, with dimensions 6 x 3 such that AR = 0(Note: Matrix R cannot be the 0 matrix.) (e) What is the column space of A? (f) What is the dimension of the column space?
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