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Addition and Subtraction of Matrices

Addition and Subtraction of Matrices – For Addition and Subtraction of two or more than two matrices there order should be same.

 

Example based on Addition of Matrices

Question 1

If A =\begin{bmatrix} 2 & 1 \\ 3 & 5 \end{bmatrix} and B = \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix}  then, find A + B ?

Explanation

Given:
A = \begin{bmatrix} 2 & 1 \\ 3 & 5 \end{bmatrix}

B = \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix}

For addition of two or more than two matrices there order should be same.
Order of Matrix A = 2 x 2
Order of Matrix B = 2 x 2

So, we add them

A + B = \begin{bmatrix} 2 & 1 \\ 3 & 5 \end{bmatrix} + \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix}

A + B = \begin{bmatrix} 2 + 1 & 1 + 3 \\ 3 + 4 & 5 + 2 \end{bmatrix}

A + B = \begin{bmatrix} 3 & 4 \\ 7 & 7 \end{bmatrix}

 

Question 2

If A = \begin{bmatrix} 3\quad & 4\quad & -6 \\ 1\quad & 2\quad & -2 \end{bmatrix} and B = \begin{bmatrix} -1\quad & 3\quad & 1 \\ -2\quad & 7\quad & 4 \end{bmatrix}  then, find A + B ?

Explanation

Given:
A = \begin{bmatrix} 3\quad & 4\quad & -6 \\ 1\quad & 2\quad & -2 \end{bmatrix}

B = \begin{bmatrix} -1\quad & 3\quad & 1 \\ -2\quad & 7\quad & 4 \end{bmatrix}

For addition of two or more than two matrices there order should be same.
Order of Matrix A = 2 x 3
Order of Matrix B = 2 x 3

So, we add them

A + B = \begin{bmatrix} 3\quad & 4\quad & -6 \\ 1\quad & 2\quad & -2 \end{bmatrix} + \begin{bmatrix} -1\quad & 3\quad & 1 \\ -2\quad & 7\quad & 4 \end{bmatrix}

A + B = \begin{bmatrix} 3\quad +\quad (-1)\quad \quad & 4\quad +\quad 3\quad \quad & -6\quad +\quad 1 \\ 1\quad +\quad (-2)\quad \quad & 2\quad +\quad 7\quad \quad & -2\quad +\quad 4 \end{bmatrix}

A + B = \begin{bmatrix} 2\quad & 7\quad & -5 \\ -1\quad & 9\quad & 2 \end{bmatrix}

 

Example based on Subtraction of Matrices

Question 1

If A =\begin{bmatrix} 7 & 6 \\ 9 & 5 \end{bmatrix} and B = \begin{bmatrix} 3 & 4 \\ 3 & 2 \end{bmatrix}  then, find A – B ?

Explanation

Given:
A = \begin{bmatrix} 7 & 6 \\ 9 & 5 \end{bmatrix}

B = \begin{bmatrix} 3 & 4 \\ 3 & 2 \end{bmatrix}

For subtraction of two or more than two matrices there order should be same.
Order of Matrix A = 2 x 2
Order of Matrix B = 2 x 2

So, we subtract them

A – B = \begin{bmatrix} 7 & 6 \\ 9 & 5 \end{bmatrix} + \begin{bmatrix} 3 & 4 \\ 3 & 2 \end{bmatrix}

A – B = \begin{bmatrix} 7 - 3 & 6 - 4 \\ 9 - 3 & 5 - 2 \end{bmatrix}

A – B = \begin{bmatrix} 4 & 2 \\ 6 & 3 \end{bmatrix}

Question 2

If A = \begin{bmatrix} 5\quad & 7\quad & 4 \\ 3\quad & 2\quad & 6 \end{bmatrix} and B = \begin{bmatrix} 2\quad & 3\quad & 6 \\ -4\quad & 7\quad & 3 \end{bmatrix}  then, find A – B ?

Explanation

Given:
A = \begin{bmatrix} 5\quad & 7\quad & 4 \\ 3\quad & 2\quad & 6 \end{bmatrix}

B = \begin{bmatrix} 2\quad & 3\quad & 6 \\ -4\quad & 7\quad & 3 \end{bmatrix}

For subtraction of two or more than two matrices there order should be same.
Order of Matrix A = 2 x 3
Order of Matrix B = 2 x 3

So, we subtract them

A – B = \begin{bmatrix} 5\quad & 7\quad & 4 \\ 3\quad & 2\quad & 6 \end{bmatrix} + \begin{bmatrix} 2\quad & 3\quad & 6 \\ -4\quad & 7\quad & 3 \end{bmatrix}

A – B = \begin{bmatrix} 5\quad -\quad 2\quad \quad & 7\quad -\quad 3\quad \quad & 4\quad -\quad 6 \\ 3\quad -\quad (-4)\quad \quad & 2\quad -\quad 7\quad \quad & 6\quad -\quad 3 \end{bmatrix}

A – B = \begin{bmatrix} 3\quad & 4\quad & -2 \\ 7\quad & -5\quad & 3 \end{bmatrix}