Linear Algebra and Fourier Analysis (Solve the question 2 completey, please don't skip) 1. Consider the matrix11 311 -12 1 -21 62 -1 0A =-31413(a) Find the row space, R(A), and column space, C(A), of A in terms of linearlyindependent rows and columns of A, respectively.(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), thenullspace of A.(b) Find the basis and dimension of N(A).1(c) If b :determine whether the nonhomogeneous system Ax = b is consis-21tent. [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 = Xp + Xpwhere 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.

Given A=113162−101−1−321−2141613.

Answered: 2. Consider the matrix A in Problem 1.…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 40EQ

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Linear Algebra and Fourier Analysis (Solve the question 2 completey, please don't skip)

1. Consider the matrix
1
1 3
1
1 -1
2 1 -2
1 6
2 -1 0
A =
-3
1
4
1
3
(a) Find the row space, R(A), and column space, C(A), of A in terms of linearly
independent rows and columns of A, respectively.
(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-
2
1
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 = Xp + 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.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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