1. Consider the matrix11 312 -1 01-1A21 -21 6-3413(a) Find row space, R(A), and column space, C(A), of A.(b) Find the bases for R(A) and C(A) obtained in 1(a).(c) Find dim(R(A)) and dim(C(A)).(d) Find the rank(A).2. Consider the matrix A in Problem 1.(a) Find the solution space of the homogeneous system Ax =nullspace of A.0, that is N(A), the(b) Find the basis and dimension of N(A).1(c) If bdetermine whether the nonhomogeneous system Ax b is consis-27tent. [Instruction: DO NOT solve Ax = b but use 1(b) to conclude.](d) If the system Ax = b is consistent where b is given in 2(c), find the completesolution in the formx = x, + X,where x, denotes a particular solution and x, denotes a solution of the associatedhomogeneous system Ax = 0.Note: It is strongly recommended to use information and results obtained in Problem1 to solve Problem 2.

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Consider the matrix 1 1 3 2 -1 0 1-1 A = -3 21 -2 16 1 1 4 3 (a) Find row space, R(A), and column space, C(A), of A. (b) Find the bases for R(A) and C(A) obtained in 1(a). (c) Find dim(R(A)) and dim(C(A)). 1.

Consider the matrix 1 1 3 2 -1 0 1-1 A = -3 21 -2 16 1 1 4 3 (a) Find row space, R(A), and column space, C(A), of A. (b) Find the bases for R(A) and C(A) obtained in 1(a). (c) Find dim(R(A)) and dim(C(A)). 1.

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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Question

1. Consider the matrix
1
1 3
1
2 -1 0
1
-1
A
21 -2
1 6
-3
4
1
3
(a) Find row space, R(A), and column space, C(A), of A.
(b) Find the bases for R(A) and C(A) obtained in 1(a).
(c) Find dim(R(A)) and dim(C(A)).
(d) Find the rank(A).
2. Consider the matrix A in Problem 1.
(a) Find the solution space of the homogeneous system Ax =
nullspace of A.
0, that is N(A), the
(b) Find the basis and dimension of N(A).
1
(c) If b
determine whether the nonhomogeneous system Ax b is consis-
2
7
tent. [Instruction: DO NOT solve Ax = b but use 1(b) to conclude.]
(d) If the system Ax = b is consistent where b is given in 2(c), find the complete
solution in the form
x = x, + X,
where x, denotes a particular solution and x, denotes a solution of the associated
homogeneous system Ax = 0.
Note: It is strongly recommended to use information and results obtained in Problem
1 to solve Problem 2.

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