1. Consider the matrix 6. 1 -1 21 -2 1 1 3 1 2 -1 0 A -3 1 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).
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![1. Consider the matrix
1
1 3
1
6
2 -1 0
1
-1
A =
-3
2 1 -2
1
4
1 6
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.
0, that is N(A), the
(a) Find the solution space of the homogeneous system Ax
nullspace of A.
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(b) Find the basis and dimension of N(A).
(с) 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
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solution in the form
x = x, + Xp,
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%2F5ca087a9-878c-43af-99c1-3cb1f27fd397%2F7ed0c668-4639-4cf6-b374-e8c51e3e7bea%2Fhsl94w_processed.jpeg&w=3840&q=75)
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