Linear algebra Determine which of the following sets are subspaces of R³.1. {[7, y, z) | y, z arbitrary numbers}.2. {[x, y, z]T| - 8x - 2y = 0,3. {[x, y, z]T | x² = z²}.Determine which of the following set are subspaces of R³×31. The 3 x 3 symmetric matrices.??????Vv3z + 5y = 0}.2. The 3 x 3 matrices with all zeros in the second row.3. The 3 x 3 singular matrices.Note: You can earn partial credit on this problem.

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Answered: ? ? Determine which of the following…

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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Linear algebra

Determine which of the following sets are subspaces of R³.
1. {[7, y, z) | y, z arbitrary numbers}.
2. {[x, y, z]T| - 8x - 2y = 0,
3. {[x, y, z]T | x² = z²}.
Determine which of the following set are subspaces of R³×3
1. The 3 x 3 symmetric matrices.
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V
v
3z + 5y = 0}.
2. The 3 x 3 matrices with all zeros in the second row.
3. The 3 x 3 singular matrices.
Note: You can earn partial credit on this problem.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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