Add the matrices
$\left[\begin{array}{cc}
4 & -1 \\
4 & 2
\end{array}\right]+\left[\begin{array}{cc}
3 & 0 \\
1 & 5
\end{array}\right]$
Answer (1)
To add two matrices, we add their corresponding elements. The sum of [ 4 − 1 4 2 ] and [ 3 0 1 5 ] is [ 7 − 1 5 7 ] . Therefore, the final answer is [ 7 − 1 5 7 ] .
Explanation
Understanding the Problem We are given two 2x2 matrices and asked to add them. The first matrix is [ 4 − 1 4 2 ] . The second matrix is [ 3 0 1 5 ] .
Adding Corresponding Elements To add two matrices, we add their corresponding elements. This means we add the element in the first row and first column of the first matrix to the element in the first row and first column of the second matrix, and so on.
Performing the Addition So, we have:
[ 4 − 1 4 2 ] + [ 3 0 1 5 ] = [ 4 + 3 − 1 + 0 4 + 1 2 + 5 ]
Simplifying the Result Now, we simplify each element:
[ 4 + 3 − 1 + 0 4 + 1 2 + 5 ] = [ 7 − 1 5 7 ]
Final Answer Therefore, the sum of the two matrices is [ 7 − 1 5 7 ] .
Examples
Matrix addition is used in various fields such as computer graphics, physics, and engineering. For example, in computer graphics, matrices are used to represent transformations such as rotations, scaling, and translations of objects. Adding matrices can combine these transformations into a single transformation. In physics, matrices can represent physical quantities such as stress and strain, and matrix addition can be used to analyze the combined effect of these quantities. In engineering, matrix addition is used in structural analysis to determine the overall forces and displacements in a structure.
