give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a. find bases for the subspace Col A , Row A , Nul A . justify your answers b. find dim(Col A) , dim(Row A ), and dim (Nul A) c. Find rank(A )+ dim(Nul A)

give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a. find bases for the subspace Col A , Row A , Nul A . justify your answers b. find dim(Col A) , dim(Row A ), and dim (Nul A) c. Find rank(A )+ dim(Nul A)

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a. find bases for the subspace Col A , Row A , Nul A . justify your answers

b. find dim(Col A) , dim(Row A ), and dim (Nul A)

c. Find rank(A )+ dim(Nul A)

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