Certainly! Let's find the matrix [tex]\( B - C \)[/tex] step by step.
First, we're given the matrices [tex]\( B \)[/tex] and [tex]\( C \)[/tex]:
[tex]\[ B = \begin{bmatrix} 2 & -3 \\ -4 & 5 \end{bmatrix} \][/tex]
[tex]\[ C = \begin{bmatrix} 1 & -3 \\ -4 & 4 \end{bmatrix} \][/tex]
To subtract matrix [tex]\( C \)[/tex] from matrix [tex]\( B \)[/tex], we subtract each element of [tex]\( C \)[/tex] from the corresponding element of [tex]\( B \)[/tex].
The subtraction is done element-wise:
1. For the element in the first row, first column:
[tex]\[ B_{11} - C_{11} = 2 - 1 = 1 \][/tex]
2. For the element in the first row, second column:
[tex]\[ B_{12} - C_{12} = -3 - (-3) = -3 + 3 = 0 \][/tex]
3. For the element in the second row, first column:
[tex]\[ B_{21} - C_{21} = -4 - (-4) = -4 + 4 = 0 \][/tex]
4. For the element in the second row, second column:
[tex]\[ B_{22} - C_{22} = 5 - 4 = 1 \][/tex]
Now, we can put these results together to form the matrix [tex]\( B - C \)[/tex]:
[tex]\[ B - C = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \][/tex]
So, the matrix [tex]\( B - C \)[/tex] is:
[tex]\[ \boxed{\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}} \][/tex]
