4.Let[2 -41 0]1 -21 -4 2A =1 -134 -7 4 -4 5(a) Do the following regarding the row space of A, R(A).(i) Describe R(A) with respect to the rows of A (no working required).(ii) By (i), identify the set B1 such that (B1) = R(A) (no working required).(iii) Discuss the relations among the vectors of B to determine the subset 7, c B, suchthat T, is linearly independent and L(T;)=R(A).(b) Support your answer in (a) by computing for the RREF of A.(c) Based on yourresult in (a), as well as in (b), determine the dimension of the column spaceof 4, C(A) and the basis T, for C(A).(d) From your results above, comment on the rank of A, p(A).

Answered: Image /qna-images/answer/b58219ca-08f5-4efc-8588-daf13d7a5952.jpg

Let 2 -4 3 1 0 1 -2 1 -4 2 1 -1 A = 3 1 4 -7 4 -4 5 Do the following regarding the row space of A, R(A). (i) Describe R(A) with respect to the rows of A (no working required). (ii) By (i), identify the set B1 such that (B1) = R(A) (no working required). (iii) Discuss the relations among the vectors of B1 to determine the subset T, CB, such that T is linearly independent and L(T¡)=R(A). Support your answer in (a) by computing for the RREF of A. Based on your result in (a), as well as in (b), determine the dimension of the column space of A, C(A) and the basis T, for C(A). From your results above, comment on the rank of A, p(A).

Let 2 -4 3 1 0 1 -2 1 -4 2 1 -1 A = 3 1 4 -7 4 -4 5 Do the following regarding the row space of A, R(A). (i) Describe R(A) with respect to the rows of A (no working required). (ii) By (i), identify the set B1 such that (B1) = R(A) (no working required). (iii) Discuss the relations among the vectors of B1 to determine the subset T, CB, such that T is linearly independent and L(T¡)=R(A). Support your answer in (a) by computing for the RREF of A. Based on your result in (a), as well as in (b), determine the dimension of the column space of A, C(A) and the basis T, for C(A). From your results above, comment on the rank of A, p(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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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

4.
Let
[2 -4
1 0]
1 -2
1 -4 2
A =
1 -1
3
4 -7 4 -4 5
(a) Do the following regarding the row space of A, R(A).
(i) Describe R(A) with respect to the rows of A (no working required).
(ii) By (i), identify the set B1 such that (B1) = R(A) (no working required).
(iii) Discuss the relations among the vectors of B to determine the subset 7, c B, such
that T, is linearly independent and L(T;)=R(A).
(b) Support your answer in (a) by computing for the RREF of A.
(c) Based on yourresult in (a), as well as in (b), determine the dimension of the column space
of 4, C(A) and the basis T, for C(A).
(d) From your results above, comment on the rank of A, p(A).

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