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Drag each value to the correct location on the matrix.

[tex]\[
A = \left[\begin{array}{ccc}
5 & 7 & 2 \\
4 & -1 & 3 \\
6 & 8 & -5
\end{array}\right], \quad B = \left[\begin{array}{ccc}
6 & 11 & -4 \\
2 & 1 & -5 \\
3 & -9 & 6
\end{array}\right]
\][/tex]

Match each value to the correct entry in matrix [tex]\( AB \)[/tex].

- 37
- 31
- [tex]\(-94\)[/tex]
- 44
- 119
- 7
- 50
- 16
- [tex]\(-43\)[/tex]

Sagot :

GinnyAnswer
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]
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