A=[ 1 2 4 3 ], B=[ -3 5 2 -1 ] 𝐂=[ 1 -1

step 1 Very similar approach. We're going to take the elements in each corresponding position and subtr

A=[ 1 2 4 3 ], B=[ -3 5 ...

\begin{aligned} &A=\left[\begin{array}{ll} 1 & 2 \\ 4 & 3 \end{array}\right], \quad B=\left[\begin{array}{rr} -3 & 5 \\ 2 & -1 \end{array}\right]\\ &\mathbf{C}=\left[\begin{array}{rr} 1 & -1 \\ -1 & 1 \end{array}\right], \quad \mathbf{D}=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]\\ &\mathbf{E}=\left[\begin{array}{ll} 1 & 3 \\ 2 & 6 \end{array}\right], \quad \mathbf{F}=\left[\begin{array}{rr} 3 & 3 \\ -1 & -1 \end{array}\right]\\ &0=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right], \quad \quad \mathbf{I}=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \end{aligned} $$\mathbf{B}-\mathbf{A}$$

\begin{aligned}
&A=\left[\begin{array}{ll}
1 & 2 \\
4 & 3
\end{array}\right], \quad B=\left[\begin{array}{rr}
-3 & 5 \\
2 & -1
\end{array}\right]\\
&\mathbf{C}=\left[\begin{array}{rr}
1 & -1 \\
-1 & 1
\end{array}\right], \quad \mathbf{D}=\left[\begin{array}{ll}
1 & 1 \\
1 & 1
\end{array}\right]\\
&\mathbf{E}=\left[\begin{array}{ll}
1 & 3 \\
2 & 6
\end{array}\right], \quad \mathbf{F}=\left[\begin{array}{rr}
3 & 3 \\
-1 & -1
\end{array}\right]\\
&0=\left[\begin{array}{ll}
0 & 0 \\
0 & 0
\end{array}\right], \quad \quad \mathbf{I}=\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right]
\end{aligned}
$$\mathbf{B}-\mathbf{A}$$

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Key Concepts

Matrix Subtraction

Matrix subtraction is a basic operation in linear algebra where corresponding entries of two matrices of the same dimensions are subtracted to form a new matrix. This operation is performed entry by entry, making it a straightforward extension of scalar subtraction to matrices.

Element-wise Operations

Element-wise operations refer to applying a computation individually to each pair of corresponding entries in the matrices. In matrix subtraction, each entry in one matrix is directly subtracted from the corresponding entry in the other matrix, ensuring that every position in the resultant matrix represents the difference of the original entries.

Dimensional Compatibility

Before performing matrix operations such as subtraction, it is crucial that the matrices involved have identical dimensions, meaning the same number of rows and columns. This compatibility ensures that every position in one matrix accurately corresponds to a position in the other, which is necessary for the element-wise operation to be valid.

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