Let's consider the matrix [tex]\( T \)[/tex]:
[tex]\[
T=\left[\begin{array}{ccccc}
0 & 3.2 & 3.5 & 0 & 5.4 \\
2.6 & 0 & 1.8 & 2.1 & 0 \\
0 & 0 & 0 & 3.8 & 0 \\
6.8 & 0 & 0 & 0 & 7 \\
0 & 0 & 0 & 6.2 & 0
\end{array}\right]
\][/tex]
### Step 1: Find the row with the smallest nonzero element.
First, let's identify all the nonzero elements in the matrix [tex]\( T \)[/tex]. These elements are:
- Row 1: [tex]\( 3.2, 3.5, 5.4 \)[/tex]
- Row 2: [tex]\( 2.6, 1.8, 2.1 \)[/tex]
- Row 3: [tex]\( 3.8 \)[/tex]
- Row 4: [tex]\( 6.8, 7 \)[/tex]
- Row 5: [tex]\( 6.2 \)[/tex]
Next, we need to find the smallest nonzero element from these values:
- Comparing [tex]\( 3.2, 3.5, 5.4, 2.6, 1.8, 2.1, 3.8, 6.8, 7, 6.2 \)[/tex], we see that [tex]\( 1.8 \)[/tex] is the smallest.
The smallest nonzero element [tex]\( 1.8 \)[/tex] is located in row 2.
Thus, the row containing the smallest nonzero element is Row 2.
### Step 2: Find the value of [tex]\( t_{34} \)[/tex].
The notation [tex]\( t_{34} \)[/tex] indicates the element located in the 3rd row and the 4th column of the matrix [tex]\( T \)[/tex]:
Looking at row 3 and column 4 of the matrix [tex]\( T \)[/tex]:
[tex]\[
T = \left[\begin{array}{ccccc}
0 & 3.2 & 3.5 & 0 & 5.4 \\
2.6 & 0 & 1.8 & 2.1 & 0 \\
0 & 0 & 0 & 3.8 & 0 \\
6.8 & 0 & 0 & 0 & 7 \\
0 & 0 & 0 & 6.2 & 0
\end{array}\right]
\][/tex]
From the 3rd row and the 4th column, the value is [tex]\( 3.8 \)[/tex].
So, the value of [tex]\( t_{34} \)[/tex] is [tex]\( 3.8 \)[/tex].
### Summary:
- The row containing the smallest nonzero element is Row 2.
- The value of [tex]\( t_{34} \)[/tex] is [tex]\( 3.8 \)[/tex].
