Answered

Drag the terms to the correct boxes to complete the pairs. Not all terms will be used.

[tex]\[
A=\left[\begin{array}{rr}
2 & -5 \\
1 & 0
\end{array}\right] \quad \text{and} \quad B=\left[\begin{array}{rr}
-2 & -5 \\
1 & 0
\end{array}\right]
\][/tex]

Match the matrix operations with the resulting matrices.

[tex]\[ 2(A+B) \][/tex]
[tex]\[ 2A + 3A \][/tex]
[tex]\[ 2(A-B) \][/tex]
[tex]\[ 2A - B \][/tex]
[tex]\[ 2A \][/tex]

[tex]\[ \left[\begin{array}{rr}6 & -5 \\ 1 & 0\end{array}\right] \longrightarrow \square \][/tex]
[tex]\[ \square \left[\begin{array}{ll}8 & 0 \\ 0 & 0\end{array}\right] \square \square \][/tex]
[tex]\[ \left[\begin{array}{cc}10 & -25 \\ 5 & 0\end{array}\right] \longrightarrow \square \][/tex]



Answer :

GinnyAnswer
Let's analyze the given matrices and their resulting matrix operations step-by-step.

The matrices provided are:
[tex]$ A = \left[\begin{array}{rr} 2 & -5 \\ 1 & 0 \end{array}\right], \quad B = \left[\begin{array}{rr} -2 & -5 \\ 1 & 0 \end{array}\right] $[/tex]

The required matrix operations are:
- [tex]$2(A + B)$[/tex]
- [tex]$2A + 3A$[/tex]
- [tex]$2(A - B)$[/tex]
- [tex]$2A - B$[/tex]
- [tex]$2A$[/tex]

And the resulting matrices are:
- [tex]$\left[\begin{array}{rr}6 & -5 \\ 1 & 0\end{array}\right]$[/tex]
- [tex]$\left[\begin{array}{cc}10 & -25 \\ 5 & 0\end{array}\right]$[/tex]
- [tex]$\left[\begin{array}{ll}8 & 0 \\ 0 & 0\end{array}\right]$[/tex]

Let's match each matrix operation to its result.

### Matching Matrix Operations with Results:

1. [tex]$2(A + B)$[/tex]:

Calculate [tex]$A + B$[/tex]:
[tex]$ A + B = \left[\begin{array}{rr} 2 & -5 \\ 1 & 0 \end{array}\right] + \left[\begin{array}{rr} -2 & -5 \\ 1 & 0 \end{array}\right] = \left[\begin{array}{rr} 0 & -10 \\ 2 & 0 \end{array}\right] $[/tex]

Now multiply by 2:
[tex]$ 2(A + B) = 2 \times \left[\begin{array}{rr} 0 & -10 \\ 2 & 0 \end{array}\right] = \left[\begin{array}{rr} 0 & -20 \\ 4 & 0 \end{array}\right] $[/tex]

The result is not among the matrices provided, so this operation doesn’t match any of our given results.

2. [tex]$2A + 3A$[/tex]:

Calculate:
[tex]$ 2A + 3A = 5A = 5 \times \left[\begin{array}{rr} 2 & -5 \\ 1 & 0 \end{array}\right] = \left[\begin{array}{rr} 10 & -25 \\ 5 & 0 \end{array}\right] $[/tex]

Matching this matrix:
[tex]$ \left[\begin{array}{cc}10 & -25 \\ 5 & 0\end{array}\right] \longrightarrow 2A + 3A $[/tex]

3. [tex]$2(A - B)$[/tex]:

Calculate [tex]$A - B$[/tex]:
[tex]$ A - B = \left[\begin{array}{rr} 2 & -5 \\ 1 & 0 \end{array}\right] - \left[\begin{array}{rr} -2 & -5 \\ 1 & 0 \end{array}\right] = \left[\begin{array}{rr} 4 & 0 \\ 0 & 0 \end{array}\right] $[/tex]

Now multiply by 2:
[tex]$ 2(A - B) = 2 \times \left[\begin{array}{rr} 4 & 0 \\ 0 & 0 \end{array}\right] = \left[\begin{array}{rr} 8 & 0 \\ 0 & 0 \end{array}\right] $[/tex]

Matching this matrix:
[tex]$ \left[\begin{array}{ll}8 & 0 \\ 0 & 0\end{array}\right] \longrightarrow 2(A - B) $[/tex]

4. [tex]$2A - B$[/tex]:

Calculate:
[tex]$ 2A - B = 2 \times \left[\begin{array}{rr} 2 & -5 \\ 1 & 0 \end{array}\right] - \left[\begin{array}{rr} -2 & -5 \\ 1 & 0 \end{array}\right] = \left[\begin{array}{rr} 4 & -10 \\ 2 & 0 \end{array}\right] - \left[\begin{array}{rr} -2 & -5 \\ 1 & 0 \end{array}\right] = \left[\begin{array}{rr} 6 & -5 \\ 1 & 0 \end{array}\right] $[/tex]

Matching this matrix:
[tex]$ \left[\begin{array}{rr}6 & -5 \\ 1 & 0\end{array}\right] \longrightarrow 2A - B $[/tex]

5. [tex]$2A$[/tex]:

Calculate:
[tex]$ 2A = 2 \times \left[\begin{array}{rr} 2 & -5 \\ 1 & 0 \end{array}\right] = \left[\begin{array}{rr} 4 & -10 \\ 2 & 0 \end{array}\right] $[/tex]
The result is not among the matrices provided, so this operation doesn’t match any of our given results.

### Summary:
- [tex]$2A - B \longrightarrow \left[\begin{array}{rr}6 & -5 \\ 1 & 0\end{array}\right]$[/tex]
- [tex]$2A + 3A \longrightarrow \left[\begin{array}{cc}10 & -25 \\ 5 & 0\end{array}\right]$[/tex]
- [tex]$2(A - B) \longrightarrow \left[\begin{array}{ll}8 & 0 \\ 0 & 0\end{array}\right]$[/tex]

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