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1. Let W be the set of matrices in M2.2 given by W 3 -20 (a) Determine whether W is linearly dependent or linearly independent. In your solution you must i. Use the definition of linear dependence/independence to derive the equations to be solved. ii. Use row operations to reduce the matrix to reduced row-echelon form. (b) Can we write one of the matrices in W as a linear combination of other matrices in W? Explain your answer. If so, express one of the matrices as a linear combination of the other matrices. (c) Does W span M2,2? Explain your answer.

1. Let W be the set of matrices in M2.2 given by W 3 -20 (a) Determine whether W is linearly dependent or linearly independent. In your solution you must i. Use the definition of linear dependence/independence to derive the equations to be solved. ii. Use row operations to reduce the matrix to reduced row-echelon form. (b) Can we write one of the matrices in W as a linear combination of other matrices in W? Explain your answer. If so, express one of the matrices as a linear combination of the other matrices. (c) Does W span M2,2? Explain your answer.

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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1. Let W be the set of matrices in M2.2 given by -1 2 W 3 -20 (a) Determine whether W is linearly dependent or linearly independent. In your solution you must i. Use the definition of linear dependence/independence to derive the equations to be solved. ii. Use row operations to reduce the matrix to reduced row-echelon form. (b) Can we write one of the matrices in W as a linear combination of other matrices in W? Explain your answer. If so, express one of the matrices as a linear combination of the other matrices. (c) Does W span M2,2? Explain your answer. (d) Find a basis for span(W) using only elements of W.
Transcribed Image Text:1. Let W be the set of matrices in M2.2 given by -1 2 W 3 -20 (a) Determine whether W is linearly dependent or linearly independent. In your solution you must i. Use the definition of linear dependence/independence to derive the equations to be solved. ii. Use row operations to reduce the matrix to reduced row-echelon form. (b) Can we write one of the matrices in W as a linear combination of other matrices in W? Explain your answer. If so, express one of the matrices as a linear combination of the other matrices. (c) Does W span M2,2? Explain your answer. (d) Find a basis for span(W) using only elements of W.
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