Certainly! Let's carefully analyze and interpret the given numerical matrix:
[tex]\[
\left[\begin{array}{ccc}
2 & 3 & 1 \\
1 & -3 & -66 \\
-4 & 5 & 9
\end{array}\right]
\][/tex]
This array represents a 3x3 matrix (a matrix with 3 rows and 3 columns). Let's break down this matrix, entry by entry, to fully understand its components.
### Row 1:
The first row is:
[tex]\[
\left[\begin{array}{ccc}
2 & 3 & 1
\end{array}\right]
\][/tex]
- The first element is 2.
- The second element is 3.
- The third element is 1.
### Row 2:
The second row is:
[tex]\[
\left[\begin{array}{ccc}
1 & -3 & -66
\end{array}\right]
\][/tex]
- The first element is 1.
- The second element (-3).
- The third element (-66).
### Row 3:
The third row is:
[tex]\[
\left[\begin{array}{ccc}
-4 & 5 & 9
\end{array}\right]
\][/tex]
- The first element (-4).
- The second element 5.
- The third element 9.
### Summary:
We can now put all the rows together to visualize the matrix in a structured format.
Matrix:
[tex]\[
\left[\begin{array}{ccc}
2 & 3 & 1 \\
1 & -3 & -66 \\
-4 & 5 & 9
\end{array}\right]
\][/tex]
This matrix has:
- 2 in the first row, first column.
- 3 in the first row, second column.
- 1 in the first row, third column.
- 1 in the second row, first column.
- -3 in the second row, second column.
- -66 in the second row, third column.
- -4 in the third row, first column.
- 5 in the third row, second column.
- 9 in the third row, third column.
Thus, we have successfully identified and transcribed each element in this 3x3 matrix. Remember, each element’s position is crucial for matrix operations such as addition, multiplication, and inversion if applicable.
