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6. Answer the following for the matrix M -1 2 1 1 1 2 -2 # and vector v = (a) Evaluate Mv. (b) Based on your answer to (a) how do you know the columns of M are dependent? Use v to give a vector combination. (c) Based on your answer to (a) how do you know the linear transformation of M is not one-to-one? (d) Solve Mx = 0.

6. Answer the following for the matrix M -1 2 1 1 1 2 -2 # and vector v = (a) Evaluate Mv. (b) Based on your answer to (a) how do you know the columns of M are dependent? Use v to give a vector combination. (c) Based on your answer to (a) how do you know the linear transformation of M is not one-to-one? (d) Solve Mx = 0.

Advanced Engineering Mathematics
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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6. Answer the following for the matrix M = 1 3 1 1 1 2 1 -2 -1 -2 2 and vector v = H (a) Evaluate Mv. (b) Based on your answer to (a) how do you know the columns of M are dependent? Use v to give a vector combination. (c) Based on your answer to (a) how do you know the linear transformation of M is not one-to-one? (d) Solve Mx = 0.
Transcribed Image Text:6. Answer the following for the matrix M = 1 3 1 1 1 2 1 -2 -1 -2 2 and vector v = H (a) Evaluate Mv. (b) Based on your answer to (a) how do you know the columns of M are dependent? Use v to give a vector combination. (c) Based on your answer to (a) how do you know the linear transformation of M is not one-to-one? (d) Solve Mx = 0.
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