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We will discuss about Negative of a Matrix.
The negative of the matrix A is the matrix (-1)A, written as β A.
For example:
Let A = [12β17β59].
Then βA = (-1) [12β17β59] = [β12175β9]
Clearly, the negative matrix is obtained by changing the signs of each element.
Solved examples on Negative of a Matrix:
1. If A = [2513] then find the negative matrix of A.
Solution:
A = [2513]
The negative matrix of A = -A
Now by changing the signs of each element of matrix A
We get [β2β5β1β3]
Therefore, the negative matrix of A = -A = [β2β5β1β3].
2. If M = [5β1β32] then find the negative matrix of M.
Solution:
M = [5β1β32]
The negative matrix of M = -M
Now by changing the signs of each element of matrix M
We get [β513β2]
Therefore, the negative matrix of A = -A = [β513β2].
3. If I = [1001] then find -I.
Solution:
I = [1001]
The negative matrix of I = -I
Now by changing the signs of each element of matrix M
We get [β100β1]
Therefore, the negative matrix of I = -I = [β100β1].
Note: A + (-A) = 0; i.e., Sum a matrix and its negative matrix = 0.
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