To solve for the values of [tex]\( a \)[/tex], [tex]\( x \)[/tex], and [tex]\( y \)[/tex] given the equation of matrix addition:
[tex]\[
\left[\begin{array}{cc}a & 2 \\ 6 & 5\end{array}\right] + \left[\begin{array}{cc}4 & x \\ 8 & y\end{array}\right] = \left[\begin{array}{cc}6 & 3 \\ 10 & 5\end{array}\right]
\][/tex]
We need to equate the corresponding elements on both sides of the equation. Let's go step-by-step to find each unknown.
1. For the element in the first row, first column:
[tex]\[
a + 4 = 6
\][/tex]
Solving for [tex]\( a \)[/tex]:
[tex]\[
a = 6 - 4
\][/tex]
[tex]\[
a = 2
\][/tex]
2. For the element in the first row, second column:
[tex]\[
2 + x = 3
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
x = 3 - 2
\][/tex]
[tex]\[
x = 1
\][/tex]
3. For the element in the second row, first column:
[tex]\[
6 + 8 = 10
\][/tex]
Solving for [tex]\( y \)[/tex]:
[tex]\[
y = 10 - 6
\][/tex]
[tex]\[
y = 4
\][/tex]
So, the values are:
[tex]\[
a = 2, \quad x = 1, \quad y = 4
\][/tex]
