To determine which matrix is equal to the given matrix [tex]\(\left[\begin{array}{rrc}-6 & -6.5 & 1.7 \\ 2 & -8.5 & 19.3\end{array}\right]\)[/tex], we will compare it with each provided option.
Given Matrix:
[tex]\[
\left[\begin{array}{rrc}-6 & -6.5 & 1.7 \\ 2 & -8.5 & 19.3\end{array}\right]
\][/tex]
Option 1:
[tex]\[
\left[\begin{array}{cc}6 & 2 \\ 6.5 & 8.5 \\ 1.7 & 19.3\end{array}\right]
\][/tex]
This matrix is of size [tex]\(3 \times 2\)[/tex] (3 rows and 2 columns), whereas the given matrix is of size [tex]\(2 \times 3\)[/tex] (2 rows and 3 columns). Therefore, they are not equal.
Option 2:
[tex]\[
\left[\begin{array}{cc}-6 & 2 \\ -6.5 & -8.5 \\ 1.7 & 19.3\end{array}\right]
\][/tex]
This matrix is also of size [tex]\(3 \times 2\)[/tex]. The dimensions do not match with the given [tex]\(2 \times 3\)[/tex] matrix, so they are not equal.
Option 3:
[tex]\[
\left[\begin{array}{ccc}6 & 6.5 & -1.7 \\ -2 & 8.5 & -19.3\end{array}\right]
\][/tex]
This matrix is of size [tex]\(2 \times 3\)[/tex], matching the dimensions of the given matrix. However, the elements do not match:
- The first element [tex]\(6 \neq -6\)[/tex]
- The second element [tex]\(6.5 \neq -6.5\)[/tex]
- The third element [tex]\(-1.7 \neq 1.7\)[/tex]
- and so on...
Therefore, the matrices are not equal.
Option 4:
[tex]\[
\left[\begin{array}{lll}-6 & -6.5 & 1.7\end{array}\right]
\][/tex]
This matrix is of size [tex]\(1 \times 3\)[/tex]. The given matrix is [tex]\(2 \times 3\)[/tex], so their dimensions do not match. Thus, they are not equal.
After comparing all options, none of the matrices provided are equal to the given matrix [tex]\(\left[\begin{array}{rrc}-6 & -6.5 & 1.7 \\ 2 & -8.5 & 19.3\end{array}\right]\)[/tex].
Therefore, there is no matrix among the given options that is equal to the given matrix. All comparisons are false.
[tex]\[
(\text{False}, \text{False}, \text{False}, \text{False})
\][/tex]
