Question

If A = $\left[\begin{array}{ccc}-1&3\\4&2\end{array}\right]$, B = $\left[\begin{array}{ccc}2&1\\3&-5\end{array}\right]$, X = $\left[\begin{array}{ccc}x_{1}&x_{2}\\x_{3}&x_{4}\end{array}\right]$ and A+ B = X then find the values of x₁, x₂, x₃, and x₄.

Answer 1

If
$A=\left[\begin{array}{ccc}-1&3\\4&2\end{array}\right]$
$B=\left[\begin{array}{ccc}2&1\\3&-5\end{array}\right]$

As A+B =X

$A+B =\left[\begin{array}{ccc}-1&3\\4&2\end{array}\right]$+ $\left[\begin{array}{ccc}2&1\\3&-5\end{array}\right]$

$A+B =\left[\begin{array}{ccc}-1+2&3+1\\4+3&2-5\end{array}\right]$

$\left[\begin{array}{ccc}-1&4\\7&-3\end{array}\right] =\left[\begin{array}{ccc}x_{1}&x_{2}\\x_{3}&x_{4}\end{array}\right]$

So

$x_{1}=-1\\\\x_{2}=4\\\\x_{3}=7\\\\x_{4}=-3$

Answer 2

Step-by-step explanation:

$If</p><p>\begin{gathered} A=\left[\begin{array}{ccc}-1&3\\4&2\end{array}\right] \end{gathered} \\ </p><p>\begin{gathered} B=\left[\begin{array}{ccc}2&1\\3&-5\end{array}\right] \end{gathered} \\ </p><p></p><p>As A+B =X</p><p> \\ </p><p>\begin{gathered} A+B =\left[\begin{array}{ccc}-1&3\\4&2\end{array}\right] \end{gathered} \begin{gathered} \left[\begin{array}{ccc}2&1\\3&-5\end{array}\right] \end{gathered}</p><p> \\ </p><p>\begin{gathered} A+B =\left[\begin{array}{ccc}-1+2&3+1\\4+3&2-5\end{array}\right] \end{gathered}</p><p> \\ </p><p>\begin{gathered}\left[\begin{array}{ccc}-1&4\\7&-3\end{array}\right] =\left[\begin{array}{ccc}x_{1}&x_{2}\\x_{3}&x_{4}\end{array}\right] \end{gathered} \\ </p><p>So</p><p></p><p>\begin{gathered}x_{1}=-1\\\\x_{2}=4\\\\x_{3}=7\\\\x_{4}=-3\\\\\end{gathered}$