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4. (a) Show that {(2, 0, 1, 1), (-1,2,3, 1), (1,0,2, -1)} is a linearly independent subset of R¹. (b) Show that 13 3 0 0 -2 2 {(1) (2) († ♂ })} is a linearly independent subset of R2×3 (c) Show that {e-1,2-4, sin(x)} 1 is a linearly independent subset of the space V of functions from R to R.

4. (a) Show that {(2, 0, 1, 1), (-1,2,3, 1), (1,0,2, -1)} is a linearly independent subset of R¹. (b) Show that 13 3 0 0 -2 2 {(1) (2) († ♂ })} is a linearly independent subset of R2×3 (c) Show that {e-1,2-4, sin(x)} 1 is a linearly independent subset of the space V of functions from R to R.

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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Part c
4. (a) Show that {(2, 0, 1, 1), (−1, 2, 3, 1), (1,0,2, -1)} is a linearly independent subset of R¹. (b) Show that 0 1 3 10-2 2-3 1 0 {( 1 ) · ( 2 ) · (3)} {(° 130 is a linearly independent subset of R2×3 (c) Show that {e-1,2-4, sin(xx)} is a linearly independent subset of the space V of functions from R to R.
Transcribed Image Text:4. (a) Show that {(2, 0, 1, 1), (−1, 2, 3, 1), (1,0,2, -1)} is a linearly independent subset of R¹. (b) Show that 0 1 3 10-2 2-3 1 0 {( 1 ) · ( 2 ) · (3)} {(° 130 is a linearly independent subset of R2×3 (c) Show that {e-1,2-4, sin(xx)} is a linearly independent subset of the space V of functions from R to R.
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