1. Let W be the set of matrices in M22 given by {E 2 W = 3 -20 0 (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 M22? Explain your answer. (d) Find a basis for span(W) using only elements of W.
1. Let W be the set of matrices in M22 given by {E 2 W = 3 -20 0 (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 M22? Explain your answer. (d) Find a basis for span(W) using only elements of W.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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