Find the sum.
$\left[\begin{array}{cc}
-3 & 0 \\
5 & -7
\end{array}\right]+\left[\begin{array}{ll}
-4 & 2 \\
-1 & 8
\end{array}\right]$
Answer (2)
Add the corresponding entries of the two matrices.
Calculate the entries: (-3 + -4), (0 + 2), (5 + -1), (-7 + 8).
Write the resulting matrix with the calculated entries.
The sum of the two matrices is [ − 7 2 4 1 ] .
Explanation
Understanding the problem We are asked to find the sum of two 2x2 matrices. To do this, we add the corresponding entries of the two matrices.
Identifying the matrices The first matrix is [ − 3 0 5 − 7 ] and the second matrix is [ − 4 2 − 1 8 ] .
Adding corresponding entries We add the corresponding entries:
Top left: − 3 + ( − 4 ) = − 7
Top right: 0 + 2 = 2
Bottom left: 5 + ( − 1 ) = 4
Bottom right: − 7 + 8 = 1
Resulting matrix Therefore, the sum of the two matrices is [ − 7 2 4 1 ] .
Examples
Matrix addition is used in various fields such as computer graphics, physics, and engineering. For example, in computer graphics, matrices can represent transformations such as rotations, scaling, and translations of objects. Adding matrices can combine these transformations to create more complex movements or effects. In physics, matrices can represent physical quantities such as stress and strain in materials. Adding matrices can then be used to analyze the combined effect of multiple stresses or strains.
To find the sum of the two matrices, we add their corresponding entries. The result of the addition is the matrix [ − 7 4 2 1 ] .
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