Linear algebra: please solve all questions correctly and handwritten In Exercises 19 and 20, find a basis for the null space andthe range of the given matrix. Then use Gram-Schmidtto obtain orthogonal bases.19.1-21-2 1-52175-12-21 -120. [ 1 3 10 11 9-1 2 5 42 -1 -1 1 421. Argue that any set of four or more nonzero vectorsin R³ cannot be an orthogonal set.

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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: please solve all questions correctly and handwritten

In Exercises 19 and 20, find a basis for the null space and
the range of the given matrix. Then use Gram-Schmidt
to obtain orthogonal bases.
19.
1-2
1-2 1-5
2175
-12-2
1 -1
20. [ 1 3 10 11 9
-1 2 5 4
2 -1 -1 1 4
21. Argue that any set of four or more nonzero vectors
in R³ cannot be an orthogonal set.

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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