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2. (a) Give an example of a non-invertible non-zero 2 x 2 matrix A with entries chosen from the set {-1, 1, 2}. The simpler, the better. Show explicitly that your matrix is not invertible. (b) With your 2 x 2 matrix A that you chose above, give two examples of distinct non-zero vectors , E R satisfying Ar Ay = 0. Show explicitly that your chosen vectors satisfies A = Aj = 0. (c) With your 2 x 2 matrix A that you chose above, give an example of a non-zero vector bER so that there exists a solution z E R to the equation Az = b. Show explicitly that A 6 has a solution.

2. (a) Give an example of a non-invertible non-zero 2 x 2 matrix A with entries chosen from the set {-1, 1, 2}. The simpler, the better. Show explicitly that your matrix is not invertible. (b) With your 2 x 2 matrix A that you chose above, give two examples of distinct non-zero vectors , E R satisfying Ar Ay = 0. Show explicitly that your chosen vectors satisfies A = Aj = 0. (c) With your 2 x 2 matrix A that you chose above, give an example of a non-zero vector bER so that there exists a solution z E R to the equation Az = b. Show explicitly that A 6 has a solution.

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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2. (a) Give an example of a non-invertible non-zero 2 x 2 matrix A with entries chosen from the set {-1,1, 2}. The simpler, the better. Show explicitly that your matrix is not invertible. (b) With your 2 x 2 matrix A that you chose above, give two examples of distinet non-zero vectors , E R? satisfying AT Ar Ag 0. Ay 0. Show explicitly that your chosen vectors satisfies %3D (c) With youur 2 x 2 matrix A that you chose above, give an example of a non-zero vector b ER so that there exists a solution E R to the equation Az = b. Show explicitly that AE E = b has a solution.
Transcribed Image Text:2. (a) Give an example of a non-invertible non-zero 2 x 2 matrix A with entries chosen from the set {-1,1, 2}. The simpler, the better. Show explicitly that your matrix is not invertible. (b) With your 2 x 2 matrix A that you chose above, give two examples of distinet non-zero vectors , E R? satisfying AT Ar Ag 0. Ay 0. Show explicitly that your chosen vectors satisfies %3D (c) With youur 2 x 2 matrix A that you chose above, give an example of a non-zero vector b ER so that there exists a solution E R to the equation Az = b. Show explicitly that AE E = b has a solution.
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