1. Consider the matrix 1 1 3 1 6 1 -1 2 1 -2 16 1 2 -1 0 1 A = -3 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)). (d) Find the rank(A).
1. Consider the matrix 1 1 3 1 6 1 -1 2 1 -2 16 1 2 -1 0 1 A = -3 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)). (d) Find the rank(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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Question
Please, Answer all the questions. Use- Question : 1 fo solving Question : 2. Read carefully. 1 is the first question and 2 is the second question.
![1. Consider the matrix
1
1 3
1
6.
2 -1 0
1
-1
A =
-3
2 1
-2
4
1 6
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecfc1b1c-e525-4cfc-93e5-91a5ae148198%2F11123827-bd26-4db7-bfbb-e091373376e7%2Fb13mt9q_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the matrix
1
1 3
1
6.
2 -1 0
1
-1
A =
-3
2 1
-2
4
1 6
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 = 0, that is N(A), the
nullspace of A.
(b) Find the basis and dimension of N(A).
1
(c) If b =
determine whether the nonhomogeneous system Ax = b is consis-
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecfc1b1c-e525-4cfc-93e5-91a5ae148198%2F11123827-bd26-4db7-bfbb-e091373376e7%2Fp6e4j6e_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the matrix A in Problem 1.
(a) Find the solution space of the homogeneous system Ax = 0, that is N(A), the
nullspace of A.
(b) Find the basis and dimension of N(A).
1
(c) If b =
determine whether the nonhomogeneous system Ax = b is consis-
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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