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Question 14 For the matrix below, find the characteristic polynomial, then find all the real eigenvalues and their multiplicities. [40-1 04-1 10 2 Question 15 Diagonalize the following matrices, if possible. -4 2 1. 6 2. 4 0 04-1 (you can use the results from Q14) 10 Question 11 What's the maximal number of linearly independent vectors that 1 2 0 3 1 2 4 -1 5 4 can be found in the null space of A = 3 6-1 8 5 4 8 -1 12 8 2 Question 12 Let B and C be two basis of V satisfying the relation b₁ = ₁+2, b2 = 3c1 - €3, 63 = []B=0, find [I]c. - 2. Find the change of basis matrix P. Assume C+-B Question 13 (True or False) If A is a 3 × 5 matrix, then any spanning set of Nul A has at least two vectors.

Question 14 For the matrix below, find the characteristic polynomial, then find all the real eigenvalues and their multiplicities. [40-1 04-1 10 2 Question 15 Diagonalize the following matrices, if possible. -4 2 1. 6 2. 4 0 04-1 (you can use the results from Q14) 10 Question 11 What's the maximal number of linearly independent vectors that 1 2 0 3 1 2 4 -1 5 4 can be found in the null space of A = 3 6-1 8 5 4 8 -1 12 8 2 Question 12 Let B and C be two basis of V satisfying the relation b₁ = ₁+2, b2 = 3c1 - €3, 63 = []B=0, find [I]c. - 2. Find the change of basis matrix P. Assume C+-B Question 13 (True or False) If A is a 3 × 5 matrix, then any spanning set of Nul A has at least two vectors.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question 14 For the matrix below, find the characteristic polynomial, then find all the real eigenvalues and their multiplicities. [40-1 04-1 10 2 Question 15 Diagonalize the following matrices, if possible. -4 2 1. 6 2. 4 0 04-1 (you can use the results from Q14) 10
Transcribed Image Text:Question 14 For the matrix below, find the characteristic polynomial, then find all the real eigenvalues and their multiplicities. [40-1 04-1 10 2 Question 15 Diagonalize the following matrices, if possible. -4 2 1. 6 2. 4 0 04-1 (you can use the results from Q14) 10
Question 11 What's the maximal number of linearly independent vectors that 1 2 0 3 1 2 4 -1 5 4 can be found in the null space of A = 3 6-1 8 5 4 8 -1 12 8 2 Question 12 Let B and C be two basis of V satisfying the relation b₁ = ₁+2, b2 = 3c1 - €3, 63 = []B=0, find [I]c. - 2. Find the change of basis matrix P. Assume C+-B Question 13 (True or False) If A is a 3 × 5 matrix, then any spanning set of Nul A has at least two vectors.
Transcribed Image Text:Question 11 What's the maximal number of linearly independent vectors that 1 2 0 3 1 2 4 -1 5 4 can be found in the null space of A = 3 6-1 8 5 4 8 -1 12 8 2 Question 12 Let B and C be two basis of V satisfying the relation b₁ = ₁+2, b2 = 3c1 - €3, 63 = []B=0, find [I]c. - 2. Find the change of basis matrix P. Assume C+-B Question 13 (True or False) If A is a 3 × 5 matrix, then any spanning set of Nul A has at least two vectors.
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