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[2 1] A2 3 0 [o 2] A3 [o and A4 4.2) Let A1 = be matrices in = M2. Answer the following questions: 4.2.1) For which values of A will S = {A1, A2, A3, A4} form a linearly independent set? Show all calculations. [a b] be a matrix in M». Set up a linear system of equations that [c_d] 4.2.2) Let B = need to be satisfied such that B is spanned by the vectors in S. 4.2.3) Use the system in question 4.2.2 to find out if there are values of A for which the set S = {A1, A2, A3, A4} will be a basis for M2. If there are such values, find them all.

[2 1] A2 3 0 [o 2] A3 [o and A4 4.2) Let A1 = be matrices in = M2. Answer the following questions: 4.2.1) For which values of A will S = {A1, A2, A3, A4} form a linearly independent set? Show all calculations. [a b] be a matrix in M». Set up a linear system of equations that [c_d] 4.2.2) Let B = need to be satisfied such that B is spanned by the vectors in S. 4.2.3) Use the system in question 4.2.2 to find out if there are values of A for which the set S = {A1, A2, A3, A4} will be a basis for M2. If there are such values, find them all.

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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[2 X A2 3 0 M2. Answer the following questions: 4.2) Let A1 2 A3 and A4 be matrices in 4.2.1) For which values of A willS = {A1, A2, A3, A4} form a linearly independent set? Show all calculations. a 4.2.2) Let B = be a matrix in M2. Set up a linear system of equations that c d need to be satisfied such that B is spanned by the vectors in S. 4.2.3) Use the system in question 4.2.2 to find out if there are values of A for which the set S {A1, A2, A3, A4} will be a basis for M22. If there are such values, find them all.
Transcribed Image Text:[2 X A2 3 0 M2. Answer the following questions: 4.2) Let A1 2 A3 and A4 be matrices in 4.2.1) For which values of A willS = {A1, A2, A3, A4} form a linearly independent set? Show all calculations. a 4.2.2) Let B = be a matrix in M2. Set up a linear system of equations that c d need to be satisfied such that B is spanned by the vectors in S. 4.2.3) Use the system in question 4.2.2 to find out if there are values of A for which the set S {A1, A2, A3, A4} will be a basis for M22. If there are such values, find them all.
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