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25. (a) Find all 2 × 2 matrices whose null space is the line 3x – 5y = 0. (b) Describe the null spaces of the following matrices: |6 2 C = D = A = B = 5

25. (a) Find all 2 × 2 matrices whose null space is the line 3x – 5y = 0. (b) Describe the null spaces of the following matrices: |6 2 C = D = A = B = 5

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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25. (a) Find all 2 ×x 2 matrices whose null space is the line 3x – 5y = 0. (b) Describe the null spaces of the following matrices: 6 2 C = 3 A B = D = 5 16. (Calculus required) Show that the following sets of functions are subspaces of F(-∞, ∞). (a) All continuous functions on (–0∞, 00). (b) All differentiable functions on (-∞, ). (c) All differentiable functions on (–o, 0) that satisfy f'+ 2f = 0. 9. Find the dimension of each of the following vector spaces. (a) The vector space of all diagonal n x n matrices. (b) The vector space of all symmetric n x n matrices. (c) The vector space of all upper triangular n x n matrices.
Transcribed Image Text:25. (a) Find all 2 ×x 2 matrices whose null space is the line 3x – 5y = 0. (b) Describe the null spaces of the following matrices: 6 2 C = 3 A B = D = 5 16. (Calculus required) Show that the following sets of functions are subspaces of F(-∞, ∞). (a) All continuous functions on (–0∞, 00). (b) All differentiable functions on (-∞, ). (c) All differentiable functions on (–o, 0) that satisfy f'+ 2f = 0. 9. Find the dimension of each of the following vector spaces. (a) The vector space of all diagonal n x n matrices. (b) The vector space of all symmetric n x n matrices. (c) The vector space of all upper triangular n x n matrices.
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