Linear Dependence with Zero Vector: A Simple Solution?

Thread starter eyehategod
Start date Nov 4, 2007
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Algebra Linear Linear algebra

In summary, linear algebra is a branch of mathematics that focuses on linear equations and their representations in vector spaces. A linear algebra problem is a mathematical problem that uses concepts and techniques from linear algebra to solve it. It has various applications in fields such as physics, engineering, computer science, economics, and statistics. The basic operations in linear algebra include addition, subtraction, scalar multiplication, vector multiplication, matrix multiplication, and matrix inversion. To solve a linear algebra problem, one needs a strong understanding of vector and matrix operations, knowledge of linear transformations, and good problem-solving skills.

Nov 4, 2007

eyehategod

I have to prove that a set that has the zero vector is linearly dependent. Can anyone help me out?

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Nov 4, 2007

Dick

Science Advisor

Homework Helper

As usual a set {x1,x2...} is linearly dependent if you can find constants (not all zero) such that c1*x1+c2*x2+...=0. What happens if there is only one vector? Doesn't that make it easy?

What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear equations and their representations in vector spaces. It involves the manipulation and analysis of vectors, matrices, and linear transformations.

What is a linear algebra problem?

A linear algebra problem is a mathematical problem that involves the use of concepts and techniques from linear algebra to solve it. These problems typically involve vectors, matrices, and linear transformations.

What are some common applications of linear algebra?

Linear algebra has various applications in fields such as physics, engineering, computer science, economics, and statistics. Some common applications include solving systems of linear equations, image and signal processing, data compression, and machine learning.

What are the basic operations in linear algebra?

The basic operations in linear algebra include addition, subtraction, scalar multiplication, vector multiplication, matrix multiplication, and matrix inversion. These operations are used to manipulate and solve problems involving vectors and matrices.

What skills are needed to solve a linear algebra problem?

To solve a linear algebra problem, one needs to have a strong understanding of vector and matrix operations, knowledge of linear transformations, and the ability to use algebraic techniques to manipulate equations and solve systems of equations. A good understanding of mathematical concepts and problem-solving skills is also essential.