please box each answer so I can distinguish the work and the answers clearly. Consider the following.--0 2A = 3 -1 32 0 1(a) Compute the characteristic polynomial of A.(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A.(c) Compute the algebraic and geometric multiplicity of each eigenvalue. Now we can finish determining det(A – A1). (Hint: To factor the cubic expression in the last step, notice byinspection in the second line that 1 = -1 is a root and use the Rational Roots Theorem.)1- a2-1 - A= (1 - 2)det(A,1) - (0)det(A12) + (2)det(A13)1- 233%3D2= (1 - A)((-1)((1 + 1)(1 – 2))) + 0 + 2((2)(1 + 2))-(1 - 1)(1 - 2) +(1 + 2)= -23 + 22 +(+ 3-(2 - 3)(2 +=To conclude, state the characteristic polynomial of A.

Now we can finish determining det(A – A1). (Hint: To factor the cubic expression in the last step, notice by inspection in the second line that 1 = -1 is a root and use the Rational Roots Theorem.) |1- 2 2 -1 - A = (1 - 2)det(A,1) - (0)det(A12) + (2)det(A13) 1 - 2 3 3 %3D = (1 - 1)((-1)((1 + A)(1 - 1))) + 0 + 2((2)(1 + 2)) -(1 - 1)(1 - 2) + (1 + 1) = -23 + 22 +( + 3 -(a - 3)(2 + = To conclude, state the characteristic polynomial of A.

Now we can finish determining det(A – A1). (Hint: To factor the cubic expression in the last step, notice by inspection in the second line that 1 = -1 is a root and use the Rational Roots Theorem.) |1- 2 2 -1 - A = (1 - 2)det(A,1) - (0)det(A12) + (2)det(A13) 1 - 2 3 3 %3D = (1 - 1)((-1)((1 + A)(1 - 1))) + 0 + 2((2)(1 + 2)) -(1 - 1)(1 - 2) + (1 + 1) = -23 + 22 +( + 3 -(a - 3)(2 + = To conclude, state the characteristic polynomial of A.

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 3EQ: In Exercises 1-12, compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a...

See similar textbooks