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In Exercises 1 through 18, determine whether the vector i is in the span V of the vectors v1, . ., īm (proceed “by inspection" if possible, and use the reduced row-echelon form if necessary). If ï is in V, find the coordinates of i with respect to the basis B = (1, . .., öm) of V, and write the coordinate vector |x |B.

In Exercises 1 through 18, determine whether the vector i is in the span V of the vectors v1, . ., īm (proceed “by inspection" if possible, and use the reduced row-echelon form if necessary). If ï is in V, find the coordinates of i with respect to the basis B = (1, . .., öm) of V, and write the coordinate vector |x |B.

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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1 1 17. 굿= ; 히 v2 = , 3 1 3 4 01
Transcribed Image Text:1 1 17. 굿= ; 히 v2 = , 3 1 3 4 01
GOAL Use the concept of coordinates. Apply the defini- tion of the matrix of a linear transformation with respect to a basis. Relate this matrix to the standard matrix of the transformation. Find the matrix of a linear transfor- mation (with respect to any basis) column by column. Use the concept of similarity. In Exercises 1 through 18, determine whether the vector i is in the span V of the vectors v1, ·.., inspection" if possible, and use the reduced row-echelon form if necessary). If x is in V, find the coordinates of i with respect to the basis B = (01, ..., im) of V, and write the coordinate vector |x B. im (proceed “by
Transcribed Image Text:GOAL Use the concept of coordinates. Apply the defini- tion of the matrix of a linear transformation with respect to a basis. Relate this matrix to the standard matrix of the transformation. Find the matrix of a linear transfor- mation (with respect to any basis) column by column. Use the concept of similarity. In Exercises 1 through 18, determine whether the vector i is in the span V of the vectors v1, ·.., inspection" if possible, and use the reduced row-echelon form if necessary). If x is in V, find the coordinates of i with respect to the basis B = (01, ..., im) of V, and write the coordinate vector |x B. im (proceed “by
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