[12 -5 11 -3 2 4 -5 15 2 Given that the matrix A = is row equivalent to 1 2 0 4 3 6 -5 19 -2 12 -5 11 -3 0 0 5 -7 8 | B: 0 0 0 0-9 0 0 0 0 0 (а) Find bases for the subspaces CoI A, Row A and Nul A .Justify your answer. (b) Find dim(Col A), dim(Row A) and dim(Nul A). Justify your answer (c) Find rank(A)+ dim(Nul A).

[12 -5 11 -3 2 4 -5 15 2 Given that the matrix A = is row equivalent to 1 2 0 4 3 6 -5 19 -2 12 -5 11 -3 0 0 5 -7 8 | B: 0 0 0 0-9 0 0 0 0 0 (а) Find bases for the subspaces CoI A, Row A and Nul A .Justify your answer. (b) Find dim(Col A), dim(Row A) and dim(Nul A). Justify your answer (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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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

[12 -5 11 -3
2 4 -5 15 2
Given that the matrix A =
is row equivalent to
1 2 0 4
3 6 -5 19 -2
12 -5 11 -3
0 0 5 -7 8
|
B:
0 0 0
0-9
0 0 0
0 0
(а)
Find bases for the subspaces CoI A, Row A and
Nul A .Justify your answer.
(b)
Find dim(Col A), dim(Row A) and dim(Nul A).
Justify your answer
(c)
Find rank(A)+ dim(Nul A).

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Solution: (a)

Further,

Null space of A:

It follows,

part (b) and (c):

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