Subtraction of Two Matrices

We will learn how to find the subtraction of two matrices.

If A and B two matrices of the same order then A – B is a matrix which is the addition of A and –B.

For Example:

Let A = \(\begin{bmatrix} 0 & 1\\ 4 & 5\\ 3 & 7 \end{bmatrix}\) and B = \(\begin{bmatrix} 2 & -6\\ 8 & 4\\ 5 & -2 \end{bmatrix}\)

Then, A – B = A + (-B) = \(\begin{bmatrix} 0 & 1\\ 4 & 5\\ 3 & 7 \end{bmatrix}\) + \(\begin{bmatrix} -2 & 6\\ -8 & -4\\ -5 & 2 \end{bmatrix}\)

= \(\begin{bmatrix} 0 - 2 & 1 + 6\\ 4 - 8 & 5 - 4\\ 3 - 5 & 7 + 2 \end{bmatrix}\)

= \(\begin{bmatrix} - 2 & 7\\ -4 & 1\\ -2  & 9 \end{bmatrix}\)

Subtraction of Two Matrices

Note: The elements of A – B can also be obtained by subtracting the elements of B from the corresponding elements of A.

For Example:

Let A = \(\begin{bmatrix} 15 & -8\\ 6 & 1 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 4\\ -1 & 3 \end{bmatrix}\)

Now subtracting the elements of B from the corresponding elements of A we get,

A – B = \(\begin{bmatrix} 15 & -8\\ 6 & 1 \end{bmatrix}\) - \(\begin{bmatrix} 1 & 4\\ -1 & 3 \end{bmatrix}\)

         = \(\begin{bmatrix} 15 - 1 & -8 - 4\\ 6 + 1 & 1 - 3 \end{bmatrix}\)

         = \(\begin{bmatrix} 14 & -12\\ 7 & -2 \end{bmatrix}\).

 

Solved Examples on Subtraction of Two Matrices:

1. If M = \(\begin{bmatrix} 2 & 5\\ -1 & 3 \end{bmatrix}\) and B = \(\begin{bmatrix} 1 & 1\\ 4 & -2 \end{bmatrix}\), find M – N.

Solution:

M – N = \(\begin{bmatrix} 2 & 5\\ -1 & 3 \end{bmatrix}\) - \(\begin{bmatrix} 1 & 1\\ 4 & -2 \end{bmatrix}\)

         = \(\begin{bmatrix} 2 & 5\\ -1 & 3 \end{bmatrix}\) + \(\begin{bmatrix} -1 & -1\\ -4 & 2 \end{bmatrix}\)

         = \(\begin{bmatrix} 2 - 1 & 5 - 1\\ -1 - 4 & 3 + 2\end{bmatrix}\)

         = \(\begin{bmatrix} 1 & 4\\ -5 & 5\end{bmatrix}\).

Matrix Subtraction

2. If X = \(\begin{bmatrix} 16 & -5\\ 4 & 1 \end{bmatrix}\) and Z = \(\begin{bmatrix} -13 & 4\\ 2 & 0 \end{bmatrix}\), find X – Z.

Solution:

X – Z = \(\begin{bmatrix} 16 & -5\\ 4 & 1 \end{bmatrix}\) -  \(\begin{bmatrix} -13 & 4\\ 2 & 0 \end{bmatrix}\)

         = \(\begin{bmatrix} 16 & -5\\ 4 & 1 \end{bmatrix}\) + \(\begin{bmatrix} 13 & -4\\ -2 & 0\end{bmatrix}\)

         = \(\begin{bmatrix} 16 + 13 & -5 - 4\\ 4 - 2 & 1 - 0\end{bmatrix}\)

         = \(\begin{bmatrix} 29 & -9\\ 2 & 1\end{bmatrix}\).






10th Grade Math

From Subtraction of Two Matrices to HOME




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 3rd Grade Math Worksheets |3rd Grade Math Sheets|3rd Grade Math Lesson

    Jan 14, 25 02:50 PM

    3rd Grade Math Worksheets
    3rd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students. Teachers and parents can also follow the worksheets to guide the students.

    Read More

  2. 3rd Grade Subtraction Worksheet | 3-Digit Subtraction Worksheets | Ans

    Jan 14, 25 01:57 PM

    Fill in the Missing Numbers Subtraction and Addition
    In 3th Grade Addition Worksheet we will solve how to subtract 3-digit numbers by expansion, subtraction of 3-digit numbers without regrouping, subtraction of 3-digit numbers with regrouping, propertie…

    Read More

  3. Facts about Subtraction | Subtraction of Small Numbers|Solved Examples

    Jan 14, 25 12:29 AM

    The operation to finding the difference between two numbers is called subtraction. Let us know some facts about subtraction which will help us to learn subtraction of large numbers. 1. Subtraction wit…

    Read More

  4. Word Problems on Subtraction |Worksheet on Subtraction Word Problems |

    Jan 14, 25 12:21 AM

    Subtraction Problem
    In word problems on subtraction we need to read the question carefully and understand what we need to find out. We know, in subtraction the larger number from which we subtract the other number (the s…

    Read More

  5. Worksheet on Estimating Sums and Differences | Find the Estimated Sum

    Jan 13, 25 01:34 PM

    Estimate the Difference
    In 4th grade worksheet on estimating sums and differences, all grade students can practice the questions on estimations.This exercise sheet on estimating sums and differences can be practiced

    Read More