Explaining Linear Dependence in 5 x 3 Matrix A

  • Thread starter Thread starter blackblanx
  • Start date Start date
  • Tags Tags
    Linearly
Click For Summary
In a 5 x 3 matrix A, there are five rows and three columns, meaning the rows can be viewed as vectors in a three-dimensional space. Since there are more vectors (rows) than dimensions (columns), at least one row must be a linear combination of the others, leading to linear dependence. This is a fundamental property of vector spaces where the number of vectors exceeds the dimension of the space. Therefore, the rows of any 5 x 3 matrix A are guaranteed to be linearly dependent. Understanding this concept is crucial for solving problems related to linear algebra and matrix theory.
blackblanx
Messages
16
Reaction score
0

Homework Statement



For Any 5 x 3 matrix A, explain why rows of A must be linearly dependent.




The Attempt at a Solution


No idea please drop a hint
 
Physics news on Phys.org
blackblanx said:

Homework Statement



For Any 5 x 3 matrix A, explain why rows of A must be linearly dependent.




The Attempt at a Solution


No idea please drop a hint
What dimension are the rows? How many of them are there?
 
Hint: you can think of the rows as vectors in a three dimensional space.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Fundamental matrix linear system equivalent to linear matrix system
  • · Replies 2 ·
Replies
2
Views
1K
Determining value of r that makes the matrix linearly dependent
  • · Replies 4 ·
Replies
4
Views
2K
Linearly independent vs dependent functions
  • · Replies 3 ·
Replies
3
Views
1K
Linear independence of Coordinate vectors as columns & rows
  • · Replies 2 ·
Replies
2
Views
2K
How to find a system of equations when the solution is given?
  • · Replies 6 ·
Replies
6
Views
2K
Linear Algebra: Parametric Solution Set
  • · Replies 5 ·
Replies
5
Views
3K
Intro to Linear Algebra - Nullspace of Rank 1 Matrix
  • · Replies 8 ·
Replies
8
Views
2K
Proving statements about matrices | Linear Algebra
  • · Replies 25 ·
Replies
25
Views
3K
[Linear Algebra] Maximal linear independent subset
  • · Replies 3 ·
Replies
3
Views
3K
Is the linear mapping T(x) one to one?
  • · Replies 4 ·
Replies
4
Views
2K