Sure, let's carefully determine the entries of the resulting matrix [tex]\( AB \)[/tex] by multiplying matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex] and placing the provided values in their corresponding positions. Given the result:
[tex]\[ AB = \begin{bmatrix}
50 & 44 & -43 \\
31 & 16 & 7 \\
37 & 119 & -94
\end{bmatrix} \][/tex]
Here is the detailed layout:
- In the first row of matrix [tex]\( AB \)[/tex]:
- The first value [tex]\( 50 \)[/tex] goes to the position [tex]\( (1,1) \)[/tex].
- The second value [tex]\( 44 \)[/tex] goes to the position [tex]\( (1,2) \)[/tex].
- The third value [tex]\( -43 \)[/tex] goes to the position [tex]\( (1,3) \)[/tex].
- In the second row of matrix [tex]\( AB \)[/tex]:
- The fourth value [tex]\( 31 \)[/tex] goes to the position [tex]\( (2,1) \)[/tex].
- The fifth value [tex]\( 16 \)[/tex] goes to the position [tex]\( (2,2) \)[/tex].
- The sixth value [tex]\( 7 \)[/tex] goes to the position [tex]\( (2,3) \)[/tex].
- In the third row of matrix [tex]\( AB \)[/tex]:
- The seventh value [tex]\( 37 \)[/tex] goes to the position [tex]\( (3,1) \)[/tex].
- The eighth value [tex]\( 119 \)[/tex] goes to the position [tex]\( (3,2) \)[/tex].
- The ninth value [tex]\( -94 \)[/tex] goes to the position [tex]\( (3,3) \)[/tex].
Thus, the completed matrix [tex]\( AB \)[/tex] is:
[tex]\[ AB = \begin{bmatrix}
50 & 44 & -43 \\
31 & 16 & 7 \\
37 & 119 & -94
\end{bmatrix} \][/tex]
