Question

Determine if the following operation on the two given matrices is defined, and if it is, determine the order of the resulting matrix.
open square bracket,
begin matrix
row 1, column 1, minus, 7
row 2, column 1, 4
row 3, column 1, 7
end matrix
, close square bracket, open square bracket,
begin matrix
row 1, column 1, minus, 1
row 1, column 2, 7
row 1, column 3, 4
row 1, column 4, 8
end matrix
, close square bracket
​

−7
4
7
​

​
[
−1
​

7
​

4
​

8
​
]
Answer
Attempt 1 out of 2

The result of the operation is

Answer 1

To determine if the operation on the two given matrices is defined, we need to first look at their dimensions:

1. The first matrix is:
\[
\begin{bmatrix}
-7 \\
4 \\
7
\end{bmatrix}
\]
This is a column matrix with dimensions \(3 \times 1\) (3 rows and 1 column).

2. The second matrix is:
\[
\begin{bmatrix}
-1 & 7 & 4 & 8
\end{bmatrix}
\]
This is a row matrix with dimensions \(1 \times 4\) (1 row and 4 columns).

Next, we can see that the operation you're trying to perform is not explicitly stated. However, common matrix operations include addition, subtraction, or multiplication.

- **Addition/Subtraction**: For two matrices to be added or subtracted, they must have the same dimensions. In this case, \(3 \times 1\) and \(1 \times 4\) are not the same dimensions, so addition or subtraction is **not defined**.

- **Multiplication**: In matrix multiplication, the number of columns in the first matrix must match the number of rows in the second matrix. The first matrix has \(1\) column and the second matrix has \(1\) row. Thus, multiplication can be performed:
\[
\begin{bmatrix}
-7 \\
4 \\
7
\end{bmatrix}
\begin{bmatrix}
-1 & 7 & 4 & 8
\end{bmatrix}
\]
The result of this multiplication will be a \(3 \times 4\) matrix (the number of rows from the first matrix and the number of columns from the second matrix).

Therefore, the operation is defined (specifically multiplication), and the order of the resulting matrix is \(3 \times 4\).