Question

Given \[A=\begin{bmatrix}\sqrt{3}&1&-1\\2&3&0\end{bmatrix}\] and \[B=\begin{bmatrix}2&\sqrt{5}&1\\-2&3&\frac{1}{2}\end{bmatrix}\], find \[A+B\].

Options

• \[\begin{bmatrix}2\sqrt{3}&\sqrt{5}&-1\\-4&9&0\end{bmatrix}\]

• \[\begin{bmatrix}\sqrt{3}-2&1-\sqrt{5}&-2\\4&0&-\frac{1}{2}\end{bmatrix}\]

• \[\begin{bmatrix}2+\sqrt{3}&1+\sqrt{5}&0\\0&6&\frac{1}{2}\end{bmatrix}\]

• \[\begin{bmatrix}2+\sqrt{3}&1+\sqrt{5}&2\\4&6&\frac{1}{2}\end{bmatrix}\]

Answer 1

Both \[A\] and \[B\] have order \[2\times3\], so their sum is defined. Adding corresponding entries gives \[-1+1=0\], \[2+(-2)=0\], and the displayed matrix.