1. Say whether the following vectors are linearly independent and whether the vectors form a basis of R³. Support your answers with reasons. (a) {(1,2,3), (-1,2,3)}. (b) (c) {(2,-2, 1), (0, 2, -2), (2, 0, -1)}. (d) {(1,2,3), (-1, 2, 3), (0, 0, 0)}. {(1, 1, 1), (1,-1,-1), (-1, 1, -1), (-1,-1, 1)}.
1. Say whether the following vectors are linearly independent and whether the vectors form a basis of R³. Support your answers with reasons. (a) {(1,2,3), (-1,2,3)}. (b) (c) {(2,-2, 1), (0, 2, -2), (2, 0, -1)}. (d) {(1,2,3), (-1, 2, 3), (0, 0, 0)}. {(1, 1, 1), (1,-1,-1), (-1, 1, -1), (-1,-1, 1)}.
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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Question
c and d please
![1. Say whether the following vectors are linearly independent and whether the vectors form a basis
of R³. Support your answers with reasons.
(a) {(1,2,3), (-1,2,3)}.
(b)
(c) {(2,-2, 1), (0, 2,-2), (2, 0, -1)}. (d)
{(1,2,3), (-1, 2, 3), (0, 0, 0)}.
{(1, 1, 1), (1,-1,-1), (-1, 1, -1), (-1,-1, 1)}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dd22a7c-6880-4a63-9133-40fb48f40bc4%2F7eddaec3-18bb-4ccc-8e4f-2d8ded439902%2Fhq4jau_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Say whether the following vectors are linearly independent and whether the vectors form a basis
of R³. Support your answers with reasons.
(a) {(1,2,3), (-1,2,3)}.
(b)
(c) {(2,-2, 1), (0, 2,-2), (2, 0, -1)}. (d)
{(1,2,3), (-1, 2, 3), (0, 0, 0)}.
{(1, 1, 1), (1,-1,-1), (-1, 1, -1), (-1,-1, 1)}.
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