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If A = \(\begin{bmatrix}-1&2\\ \ \ \ 3&4\end{bmatrix}\) and B = \(\begin{bmatrix}1&2\\1&0\end{bmatrix}\), then A + B = ?

  1. \(\begin{bmatrix}-2&0\\ \ \ \ 2&4\end{bmatrix}\)
  2. \(\begin{bmatrix}0&4\\4&4\end{bmatrix}\)
  3. \(\begin{bmatrix}-1&4\\ \ \ \ 3&0\end{bmatrix}\)
  4. \(\begin{bmatrix}1&0\\0&1\end{bmatrix}\)

Answer (Detailed Solution Below)

Option 2 : \(\begin{bmatrix}0&4\\4&4\end{bmatrix}\)
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Detailed Solution

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Concept:

Matrix Addition/Subtraction:

  • Two matrices may be added or subtracted only if they have the same dimensions ("like" matrices); that is, they must have the same number of rows and columns.
  • Addition or subtraction is accomplished by adding or subtracting corresponding elements (same positions).

 

Calculation:

Given that A = \(\begin{bmatrix}-1&2\\ \ \ \ 3&4\end{bmatrix}\) and B = \(\begin{bmatrix}1&2\\1&0\end{bmatrix}\).

Now, A + B = \(\begin{bmatrix}-1+1&2+2\\ \ \ \ 3+1&4+0\end{bmatrix}\)

= \(\begin{bmatrix}0&4\\4&4\end{bmatrix}\)

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