Solving Matrices with Standard Base Formula for Ker (T)

  • Thread starter transgalactic
  • Start date
  • Tags
    Matrices
In summary, the conversation discusses the process of finding the kernel (ker) of a matrix using a given formula and the standard base. The individual has attempted to solve the problem and shares a link where they have tried to find the kernel, but have only received all zeros. They express confusion and ask for help in finding the correct answer, as their current solution does not match the answer in the book.
  • #1
transgalactic
1,395
0
i am given a formula and asked to find the ker
of the matrices of the standart base

this is the link were i tried to solve it:

http://img297.imageshack.us/my.php?image=img7979ds0.jpg

when i try to find the ker (T)

i get all zeros

i don't know where i get it wrong

my theory says that after we simplify the matrix
A*(x,y,z)=(0,0,0)

so i built equation and all i get is all zeros
and that not the answer in the book
where did i got it wrong?
 
Physics news on Phys.org
  • #2
how to find ker (t) ??
 

1. What is the standard base formula for solving matrices in Ker (T)?

The standard base formula for solving matrices in Ker (T) is to first find the null space of the matrix, which is the set of all vectors that when multiplied by the matrix result in a zero vector. Then, the basis for Ker (T) is found by selecting a set of linearly independent vectors from the null space.

2. How is the null space of a matrix calculated?

The null space of a matrix can be calculated by reducing the matrix to row echelon form and finding the columns with pivot positions. These columns correspond to the vectors in the null space. Alternatively, the null space can be found by solving the homogeneous system of equations Ax = 0, where A is the matrix in question.

3. Can the standard base formula be used for all matrices?

No, the standard base formula for Ker (T) can only be used for square matrices, as the null space and basis for Ker (T) are only defined for square matrices.

4. How do I know if my basis for Ker (T) is correct?

A basis for Ker (T) is correct if the vectors in the basis span the null space of the matrix and are linearly independent. This can be checked by multiplying the basis vectors by the matrix and verifying that the resulting vectors are all zero and by checking that the vectors in the basis are not multiples of each other.

5. Are there any practical applications for solving matrices with the standard base formula for Ker (T)?

Yes, the standard base formula is commonly used in linear algebra and can have practical applications in fields such as engineering, physics, and computer science. It can be used to solve systems of linear equations, analyze linear transformations, and find solutions to optimization problems.

Similar threads

Proving statements about matrices | Linear Algebra
    • Calculus and Beyond Homework Help
Replies
25
Views
2K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
    • Calculus and Beyond Homework Help
Replies
14
Views
588
How do I calculate the bases for Im(f) and Ker(f)?
    • Calculus and Beyond Homework Help
Replies
26
Views
6K
Matrices M such that M^2 = 0 ?
    • Calculus and Beyond Homework Help
Replies
27
Views
3K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
    • Calculus and Beyond Homework Help
Replies
2
Views
379
Linear Algebra - Kernel and range of T
    • Calculus and Beyond Homework Help
Replies
5
Views
1K
Are Similar Matrices' Eigenvalues the Same? Solving for Symmetric Matrices
    • Calculus and Beyond Homework Help
Replies
9
Views
1K
MHB Solving Overdetermined Matrices Without SVD
    • Linear and Abstract Algebra
Replies
1
Views
705
Linear Tranformation: Find the kernel of T
    • Calculus and Beyond Homework Help
Replies
8
Views
2K
[LinAlg] Set Notation, Subspaces, Bases, Ranges, & Kernels
    • Calculus and Beyond Homework Help
Replies
9
Views
1K

Hot Threads

Recent Insights

Back
Top