1. Linear independence and rank Consider 4 column vectors: 0·60-0- and 2 with x, y, z ER. i. Identify values of x, y, z such that the four vectors are linearly independent. Be sure to provid reasoning (e.g., along the lines of the statement in 4.1.4 of the Study Guide) and demonstrat that linear independence is satisfied. ii. Identify values of x, y, z such that the four vectors are linearly dependent, but any three c the vectors taken together are linearly independent. iii. In part (ii), showing the rank of the 4 × 4 matrix formed from your vectors to be 3 woul
1. Linear independence and rank Consider 4 column vectors: 0·60-0- and 2 with x, y, z ER. i. Identify values of x, y, z such that the four vectors are linearly independent. Be sure to provid reasoning (e.g., along the lines of the statement in 4.1.4 of the Study Guide) and demonstrat that linear independence is satisfied. ii. Identify values of x, y, z such that the four vectors are linearly dependent, but any three c the vectors taken together are linearly independent. iii. In part (ii), showing the rank of the 4 × 4 matrix formed from your vectors to be 3 woul
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. Linear independence and rank
Consider 4 column vectors:
1
2
X
y
2
and
1
with x, y, z € R.
i. Identify values of x, y, z such that the four vectors are linearly independent. Be sure to provide
reasoning (e.g., along the lines of the statement in 4.1.4 of the Study Guide) and demonstrate
that linear independence is satisfied.
ii. Identify values of x, y, z such that the four vectors are linearly dependent, but any three of
the vectors taken together are linearly independent.
iii. In part (ii), showing the rank of the 4 × 4 matrix formed from your vectors to be 3 would
not generally be a sufficient argument. Why not?
S
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