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
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
Transcribed Image Text: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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