Answer
The expression (A - D) is defined, and its entries are:
$| 4 \space\space 4 \space\space 4|$
$| 3 \space\space 3 \space\space 3|$
Work Step by Step
1. Check if the expression is defined.
For a subtraction, both matrices must have the same dimensions.
$A$ is a $2 \times 3$ matrix and $D$ is a $2 \times 3 $ matrix.
- The expression is defined.
2. Evaluate it:
We need to determine the $(A - D)$ matrix, to do so, we need to subtract the corresponding entries:
$(A - D)_{11} = A_{11} - D_{11} = 1 - (-3) = 1 + 3 = 4$
$(A - D)_{12} = A_{12} - D_{12} = 2 - (-2) = 2 + 2 = 4$
$(A - D)_{13} = A_{13} - D_{13} = 3 - (-1) = 3 + 1 = 4$
$(A - D)_{21} = A_{21} - D_{21} = 4 - 1 = 3 $
$(A - D)_{22} = A_{22} - D_{22} = 5 - 2 = 3 $
$(A - D)_{23} = A_{23} - D_{23} = 6 - 3 = 3 $
Now, write the $(A-D)$ matrix:
$| 4 \space\space 4 \space\space 4|$
$| 3 \space\space 3 \space\space 3|$
