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1. If [tex]$A=\left[\begin{array}{cc}4 & 2 \\ -1 & 0\end{array}\right], B=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$[/tex], find [tex]$2A + B$[/tex].

Sagot :

To find [tex]\( 2A + B \)[/tex] where [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are given matrices, we will follow these steps:

1. Matrix [tex]\( A \)[/tex]:
[tex]\[ A = \left[\begin{array}{cc}4 & 2 \\ -1 & 0\end{array}\right] \][/tex]

2. Matrix [tex]\( B \)[/tex]:
[tex]\[ B = \left[\begin{array}{cc}1 & 2 \\ 3 & 4\end{array}\right] \][/tex]

3. Calculate [tex]\( 2A \)[/tex]:
To find [tex]\( 2A \)[/tex], multiply each element of matrix [tex]\( A \)[/tex] by 2:
[tex]\[ 2A = 2 \cdot \left[\begin{array}{cc}4 & 2 \\ -1 & 0\end{array}\right] = \left[\begin{array}{cc}2 \cdot 4 & 2 \cdot 2 \\ 2 \cdot (-1) & 2 \cdot 0\end{array}\right] = \left[\begin{array}{cc}8 & 4 \\ -2 & 0\end{array}\right] \][/tex]

4. Add [tex]\( 2A \)[/tex] and [tex]\( B \)[/tex]:
Now add matrix [tex]\( B \)[/tex] to [tex]\( 2A \)[/tex]:
[tex]\[ 2A + B = \left[\begin{array}{cc}8 & 4 \\ -2 & 0\end{array}\right] + \left[\begin{array}{cc}1 & 2 \\ 3 & 4\end{array}\right] = \left[\begin{array}{cc}8 + 1 & 4 + 2 \\ -2 + 3 & 0 + 4\end{array}\right] \][/tex]

5. Compute each element of the resulting matrix:
[tex]\[ 2A + B = \left[\begin{array}{cc}9 & 6 \\ 1 & 4\end{array}\right] \][/tex]

So, the resulting matrix [tex]\( 2A + B \)[/tex] is:
[tex]\[ \left[\begin{array}{cc}9 & 6 \\ 1 & 4\end{array}\right] \][/tex]
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