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Problem 2 Which of the following sets are linearly independent? Prove your assertions. {(-12 1) (1 1). (1 3). (²4 4)} " (2) {x³ + 2x²,-x² + 3x + 1, x³ – x² + 2x − 1} in P3(R). (3) {cos²(x), sin²(x), cos(2x)} in C(R, R), where C'(R, R) is the set of all continuous function on R. in M2₂ (R).

Problem 2 Which of the following sets are linearly independent? Prove your assertions. {(-12 1) (1 1). (1 3). (²4 4)} " (2) {x³ + 2x²,-x² + 3x + 1, x³ – x² + 2x − 1} in P3(R). (3) {cos²(x), sin²(x), cos(2x)} in C(R, R), where C'(R, R) is the set of all continuous function on R. in M2₂ (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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Problem 2 Which of the following sets are linearly independent? Prove your assertions. -1 2 (1) {(129). (1). (1 3) (²44)} in M₂(R). " -2 (2) {x³ + 2x²,−x² + 3x + 1, x³ − x² + 2x − 1} in P3(R). (3) {cos²(x), sin²(x), cos(2x)} in C(R, R), where C(R, R) is the set of all continuous function on R.
Transcribed Image Text:Problem 2 Which of the following sets are linearly independent? Prove your assertions. -1 2 (1) {(129). (1). (1 3) (²44)} in M₂(R). " -2 (2) {x³ + 2x²,−x² + 3x + 1, x³ − x² + 2x − 1} in P3(R). (3) {cos²(x), sin²(x), cos(2x)} in C(R, R), where C(R, R) is the set of all continuous function on R.
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