In this article let us learn what is a matrix and how to add and subtract matrices.
What is a matrix:
Consider a set of entries or elements. When they are arranged in rows and columns enclosing them with a square bracket [ ] or parenthesis ( ) is called as matrix.
We can denote matrix using capital letters like A, B, C...
The set of entries or elements in the matrix could be real or complex numbers, algebraic expressions.
In matrix, Counting the horizontal segment from top to bottom is termed as number of rows.
Counting the vertical segment from left to right is termed as number of columns.
Example:
R1,R2,R3 represent rows
C1,C2,C3 represent columns.
Rules to be Followed while Adding and Subtracting Matrices:
When the matrices have same number of rows and columns, then we can add them.
For example:
Any two matrices of 5 rows and 3 columns could be added.
When a matrix with 2 rows and 3 columns and a matrix with 3 rows and 4 columns could not be added.
Add the corresponding rows and columns of the given two matrix and the resulatat matrix is the added matrix.
Example:
We could add or subtract the element in the third row and second column of the first matrix with the element in the third row and second column of the second matrix and not with any other entries. that is , corresponding entries are added or subtracted. For example the element in the first row first column of the first matrix can be added to the element in the first row first column in the second matrix.
Subtraction is nothing but negative addition.
Additive inverse of matrix A is - A
A + ( -A ) = ( -A ) + A = zero matrix
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Problems on Adding and Subtracting Matrices:
Let us add and subtract the given matrices
A = `[[2,5,7],[0,8,1]]` : B = `[[6,3,6],[0,3,5]]`
A+B = `[[2+6,5+3,7+6],[0+0,8+3,1+5]]`
= `[[8,8,13],[0,11,6]]`
A - B = `[[2-6,5-3,7-6],[0-0,8-3,1-5]]`
= `[[-4,2,1],[0,5,-4]]`
