Sure, let's work through the given problem step-by-step.
We are given the matrix [tex]\( B \)[/tex]:
[tex]\[ B = \begin{bmatrix}
-1 & 2 & 7 \\
-5 & 1 & 0 \\
2 & 3 & 2
\end{bmatrix} \][/tex]
Here is a detailed step-by-step construction of the matrix [tex]\( B \)[/tex]:
1. Identify the components of the matrix: The matrix [tex]\( B \)[/tex] is a 3x3 matrix, meaning it has 3 rows and 3 columns.
2. Fill in each element of the matrix:
- The element in the first row and first column (1,1) is [tex]\(-1\)[/tex].
- The element in the first row and second column (1,2) is [tex]\(2\)[/tex].
- The element in the first row and third column (1,3) is [tex]\(7\)[/tex].
This fills the first row: [tex]\([-1, 2, 7]\)[/tex].
- The element in the second row and first column (2,1) is [tex]\(-5\)[/tex].
- The element in the second row and second column (2,2) is [tex]\(1\)[/tex].
- The element in the second row and third column (2,3) is [tex]\(0\)[/tex].
This fills the second row: [tex]\([-5, 1, 0]\)[/tex].
- The element in the third row and first column (3,1) is [tex]\(2\)[/tex].
- The element in the third row and second column (3,2) is [tex]\(3\)[/tex].
- The element in the third row and third column (3,3) is [tex]\(2\)[/tex].
This fills the third row: [tex]\([2, 3, 2]\)[/tex].
3. Combine all rows to form the matrix [tex]\( B \)[/tex]:
[tex]\[ B = \begin{bmatrix}
-1 & 2 & 7 \\
-5 & 1 & 0 \\
2 & 3 & 2
\end{bmatrix} \][/tex]
Thus, the matrix [tex]\( B \)[/tex] is:
[tex]\[
B = \begin{bmatrix}
-1 & 2 & 7 \\
-5 & 1 & 0 \\
2 & 3 & 2
\end{bmatrix}
\][/tex]
And there is our detailed construction of the given matrix!
