Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 15, 2023

Find the difference between two 2x2 matrices $A$ and $B$ .

STEP 1

Assumptions1. A and B are matrices of the same dimensions (x). . Subtraction of matrices is done element-wise, i.e., corresponding elements of the matrices are subtracted.

STEP 2

The subtraction of two matrices is done by subtracting the corresponding elements in the two matrices. The operation is defined as follows $C = B - A = \left[\begin{array}{ll} b_{11} - a_{11} & b_{12} - a_{12} \\ b_{21} - a_{21} & b_{22} - a_{22} \end{array}\right]$ where $C$ is the resulting matrix, $A$ and $B$ are the matrices being subtracted, and $a_{ij}$ and $b_{ij}$ are the elements of matrices $A$ and $B$ respectively.

STEP 3

Now, we can substitute the given matrices $A$ and $B$ into the formula.
$C = \left[\begin{array}{ll} -7 - &5 -2 \\ 2 - & -3 -9\end{array}\right]$

STEP 4

Calculate the values for each element in the resulting matrix $C$ .
$C = \left[\begin{array}{ll} -7 -4 & -2 \\ 2 -4 & -3 -9\end{array}\right] = \left[\begin{array}{ll} -11 &3 \\ -2 & -12\end{array}\right]$ So, $B - A = \left[\begin{array}{ll} -11 &3 \\ -2 & -12\end{array}\right]$ .

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