linear algebra Remember that:A subspace is never empty, and is either the just the zero vector, i.e. {0}, or has an infinitenumber of vectors.A basis for a subspace is a set of t vectors, where t is the dimension of the subspace(Usually a small number.) These vectors span the subspace and are linearly independent.This means that 0 can never part of a basis. The basis of the subspace {0} is empty, i.e. { }.A subspace can be written as all linear combination of its basis vectors, though it isUsually enough to just give the basis.1. Consider a 12-by-9 matrix of rank 7. What are the dimensions of the four fundamentalsubspaces associated with this matrix?2. Find a basis for each of the four fundamental subspaces associated with this matrix:[36.2125.3. Find a basis for each of the four fundamental subspaces associated with this matrix:1-1-2-47-63106.12-2-4]

Let A be the matrix of dimension 12-by-9, with rank 7. Since the rank of A is 7, the number of…

Answered: 1. Consider a 12-by-9 matrix of rank 7.…

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

Remember that:
A subspace is never empty, and is either the just the zero vector, i.e. {0}, or has an infinite
number of vectors.
A basis for a subspace is a set of t vectors, where t is the dimension of the subspace
(Usually a small number.) These vectors span the subspace and are linearly independent.
This means that 0 can never part of a basis. The basis of the subspace {0} is empty, i.e. { }.
A subspace can be written as all linear combination of its basis vectors, though it is
Usually enough to just give the basis.
1. Consider a 12-by-9 matrix of rank 7. What are the dimensions of the four fundamental
subspaces associated with this matrix?
2. Find a basis for each of the four fundamental subspaces associated with this matrix:
[3
6.
2
12
5.
3. Find a basis for each of the four fundamental subspaces associated with this matrix:
1
-1
-2
-4
7
-6
3
10
6.
12
-2
-4]

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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