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Adding and subtracting matrices

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Engineering Maths B, Matrices
August 8th, 2008 by Craig Rose
Permalink: http://www.craigsmaths.com/ea003-engineering-mathematics-b/adding-and-subtracting-matrices/

Engineering Maths B, Matrices
August 8th, 2008 by Craig Rose
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Matrix addition and subtraction is fairly simple. Just remember that we can only add or subtract matrices if they have the same dimensions. The number of rows must be equal in each matrix and the number of columns must be equal in each matrix.

Adding Matrices

To add matrices simply add the corresponding terms in each matrix.

Example

Given:

$\mathit{A}=\begin{bmatrix}3 & -2 & 0\\4 & -2 & 5<br /> \end{bmatrix}$

and

$\mathit{B}=\begin{bmatrix}6 & -1 & 2\\0 & -4 & 1<br /> \end{bmatrix}$

$\mathit{A}+\mathit{B}=\begin{bmatrix}4 & -2 & 5\\3 & -2 & 0<br /> \end{bmatrix}+\begin{bmatrix}6 & -1 & 2\\0 & -4 & 1<br /> \end{bmatrix}$

$=\begin{bmatrix}4+6 & -2+(-1) & 5+2\\3+0 & -2+(-4) & 0+1<br /> \end{bmatrix}$

$=\begin{bmatrix}10 & -3 & 7\\3 & -6 & 1<br /> \end{bmatrix}$

Subtracting Matrices

To subtract matrices simply subtract the corresponding terms in each matrix.

Example

With the same matrices $\mathit{A}$ and $\mathit{B}$ used in the addition example:

$\mathit{A}-\mathit{B}=\begin{bmatrix}4 & -2 & 5\\3 & -2 & 0<br /> \end{bmatrix}-\begin{bmatrix}6 & -1 & 2\\0 & -4 & 1<br /> \end{bmatrix}$

$=\begin{bmatrix}4-6 & -2-(-1) & 5-2\\3-0 & -2-(-4) & 0-1<br /> \end{bmatrix}$

$=\begin{bmatrix}-2 & -1 & 3\\3 & 2 & -1<br /> \end{bmatrix}$

Tags: adding matrices, maths tutor hobart, subtracting matrices

Friday, August 8th, 2008 at 3:05 pm
Category: Engineering Maths B, Matrices.
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