How Does Row Reduction Show that det(H) = 0 for Matrix H = Q - nI?

In summary, a matrix proof is a method of proving mathematical statements using matrices by manipulating their properties. When approaching a matrix proof, it is important to understand the properties and rules of matrices and carefully analyze the given statement. Some common properties used in matrix proofs include the commutative, associative, and distributive properties, as well as properties of matrix addition and multiplication. A successful matrix proof requires showing each step clearly and logically and double checking for errors.
  • #1
j3n
3
0
PLEASE HELP! a matrix proof..

Hey!

I really need help with this question if possible.

Let Q be an n x n matrix with each entry = 1
Let I be the n x n identity matrix
let H = Q-n*I
show that det(H) = 0

(hint: think of row reducing H)

Thanks a lot,
j3n
 
Physics news on Phys.org
  • #2
The hint pretty much tells you what to do. This might help: What is the sum of each column?
 

FAQ: How Does Row Reduction Show that det(H) = 0 for Matrix H = Q - nI?

1. What is a matrix proof?

A matrix proof is a method of proving mathematical statements using matrices. It involves manipulating matrices and their properties to show that the statement is true.

2. How do you approach a matrix proof?

When approaching a matrix proof, it is important to first understand the properties and rules of matrices. Then, carefully analyze the given statement and determine which properties can be used to prove its truth.

3. What are some common properties used in matrix proofs?

Some common properties used in matrix proofs include the commutative, associative, and distributive properties, as well as the properties of matrix addition, scalar multiplication, and matrix multiplication.

4. Can you provide an example of a matrix proof?

Sure, here is an example: Prove that (A+B)^T = A^T + B^T, where A and B are matrices of the same size.

Proof: (A+B)^T = (A+B) (using the distributive property of matrix multiplication) = A^T + B^T (using the distributive property of scalar multiplication) = A^T + B^T (therefore, (A+B)^T = A^T + B^T)

5. What are some tips for successfully completing a matrix proof?

Some tips for successfully completing a matrix proof include: understanding the properties of matrices, carefully analyzing the given statement and determining which properties can be used, showing each step of the proof clearly and logically, and double checking your work for any errors or mistakes.

Similar threads

Prove that a matrix can be reduced to RRE and CRE
Replies
4
Views
2K
How Do Matrix ODEs Relate to Determinants and Traces?
Replies
3
Views
1K
Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
Replies
3
Views
970
Showing that S is an Eigenvalue of a Matrix
Replies
4
Views
2K
Determinant of a Block Lower Triangular Matrix
Replies
2
Views
4K
B Is it invalid to redefine the sgn function in this way in a proof?
Replies
15
Views
4K
Proof: Eigenvalue λ = 0 for Non-Invertible Matrix A
Replies
5
Views
2K
Is There a Simple Way to Show GL(n,C) is a Lie Group?
Replies
4
Views
1K
Prove trace of matrix: Tr(AB) = Tr(BA)
Replies
5
Views
10K
How can I prove that A=0 using elementary operations?
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top