Let's break down the problem step-by-step and find the required information from the given matrix [tex]\( T \)[/tex]:
1. Finding the row that contains the smallest nonzero element:
The matrix [tex]\( T \)[/tex] is given as:
[tex]\[
T = \begin{pmatrix}
0 & 3.2 & 3.5 & 0 & 5.4 \\
2.6 & 0 & 1.8 & 2.1 & 0 \\
0 & 0 & 0 & 3.8 & 0 \\
6.8 & 0 & 0 & 0 & 7.0 \\
0 & 0 & 0 & 6.2 & 0
\end{pmatrix}
\][/tex]
The smallest nonzero element in this matrix is [tex]\( 1.8 \)[/tex], and it is located in the second row (index 1, considering zero-based indexing).
Row that contains the smallest nonzero element: Row 2
2. Finding the value of [tex]\( t_{34} \)[/tex]:
The value [tex]\( t_{34} \)[/tex] refers to the element in the 3rd row and 4th column of the matrix [tex]\( T \)[/tex].
Looking at the matrix, [tex]\( t_{34} = 3.8 \)[/tex].
Value of [tex]\( t_{34} \)[/tex]: 3.8
3. Finding the size of the matrix [tex]\( T \)[/tex]:
Matrix [tex]\( T \)[/tex] has rows and columns that need to be counted. The matrix is quite clearly a 5 by 5 matrix.
Size of the matrix [tex]\( T \)[/tex]:
[tex]\[
5 \times 5
\][/tex]
4. Finding the number of elements in matrix [tex]\( T \)[/tex]:
Since the matrix is of size [tex]\( 5 \times 5 \)[/tex], the total number of elements is [tex]\( 5 \times 5 = 25 \)[/tex].
Number of elements in matrix [tex]\( T \)[/tex]: 25
To summarize:
- The row that contains the smallest nonzero element is Row 2.
- The value of [tex]\( t_{34} \)[/tex] is 3.8.
- The size of matrix [tex]\( T \)[/tex] is [tex]\( 5 \times 5 \)[/tex].
- The number of elements in matrix [tex]\( T \)[/tex] is 25.
