Subtract the matrices
[tex]$\left[\begin{array}{cc}
4 & 11 \\
3 & -2
\end{array}\right]-\left[\begin{array}{cc}
10 & 3 \\
-1 & 5
\end{array}\right]$[/tex]
Answer (2)
Subtract corresponding elements of the two matrices.
Calculate: 4 − 10 = − 6 , 11 − 3 = 8 , 3 − ( − 1 ) = 4 , − 2 − 5 = − 7 .
Form the resulting matrix with the calculated elements.
The final answer is [ − 6 8 4 − 7 ] .
Explanation
Understanding the problem We are asked to subtract two 2x2 matrices. The first matrix is [ 4 11 3 − 2 ] and the second matrix is [ 10 3 − 1 5 ] . To subtract the second matrix from the first, we subtract the corresponding elements of the two matrices.
Performing the subtraction We subtract the corresponding elements:
4 − 10 = − 6
11 − 3 = 8
3 − ( − 1 ) = 3 + 1 = 4
− 2 − 5 = − 7
Resulting Matrix The resulting matrix is [ − 6 8 4 − 7 ] .
Examples
Matrix subtraction is used in various fields such as computer graphics, engineering, and economics. For example, in computer graphics, subtracting matrices can be used to calculate the difference between two images or to perform transformations on objects. In economics, it can be used to analyze changes in economic indicators over time. Understanding matrix subtraction helps in comparing and analyzing data in a structured way.
To subtract the two matrices, we subtract corresponding elements, resulting in [ − 6 4 8 − 7 ] . The process involves taking each entry in the first matrix and subtracting the corresponding entry in the second matrix. Thus, the final answer is the new matrix formed by these subtractions.
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