Answer :
Let's focus on filling in the missing values [tex]\( U \)[/tex], [tex]\( V \)[/tex], and [tex]\( W \)[/tex] in the table corresponding to [tex]\( a - b \)[/tex].
We are given:
[tex]\[ \begin{array}{|c|c|c|c|} \hline a & b & a+b & a-b \\ \hline 1 & 2 & 3 & -1 \\ \hline -1 & -2 & -3 & U \\ \hline -4 & 1 & -3 & V \\ \hline -6 & -3 & -9 & W \\ \hline \end{array} \][/tex]
### Finding [tex]\( U \)[/tex]
For [tex]\( a = -1 \)[/tex] and [tex]\( b = -2 \)[/tex]:
[tex]\[ a - b = -1 - (-2) = -1 + 2 = 1 \][/tex]
So, [tex]\( U = 1 \)[/tex].
### Finding [tex]\( V \)[/tex]
For [tex]\( a = -4 \)[/tex] and [tex]\( b = 1 \)[/tex]:
[tex]\[ a - b = -4 - 1 = -5 \][/tex]
So, [tex]\( V = -5 \)[/tex].
### Finding [tex]\( W \)[/tex]
For [tex]\( a = -6 \)[/tex] and [tex]\( b = -3 \)[/tex]:
[tex]\[ a - b = -6 - (-3) = -6 + 3 = -3 \][/tex]
So, [tex]\( W = -3 \)[/tex].
Thus, the completed table is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline a & b & a+b & a-b \\ \hline 1 & 2 & 3 & -1 \\ \hline -1 & -2 & -3 & 1 \\ \hline -4 & 1 & -3 & -5 \\ \hline -6 & -3 & -9 & -3 \\ \hline \end{array} \][/tex]
We are given:
[tex]\[ \begin{array}{|c|c|c|c|} \hline a & b & a+b & a-b \\ \hline 1 & 2 & 3 & -1 \\ \hline -1 & -2 & -3 & U \\ \hline -4 & 1 & -3 & V \\ \hline -6 & -3 & -9 & W \\ \hline \end{array} \][/tex]
### Finding [tex]\( U \)[/tex]
For [tex]\( a = -1 \)[/tex] and [tex]\( b = -2 \)[/tex]:
[tex]\[ a - b = -1 - (-2) = -1 + 2 = 1 \][/tex]
So, [tex]\( U = 1 \)[/tex].
### Finding [tex]\( V \)[/tex]
For [tex]\( a = -4 \)[/tex] and [tex]\( b = 1 \)[/tex]:
[tex]\[ a - b = -4 - 1 = -5 \][/tex]
So, [tex]\( V = -5 \)[/tex].
### Finding [tex]\( W \)[/tex]
For [tex]\( a = -6 \)[/tex] and [tex]\( b = -3 \)[/tex]:
[tex]\[ a - b = -6 - (-3) = -6 + 3 = -3 \][/tex]
So, [tex]\( W = -3 \)[/tex].
Thus, the completed table is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline a & b & a+b & a-b \\ \hline 1 & 2 & 3 & -1 \\ \hline -1 & -2 & -3 & 1 \\ \hline -4 & 1 & -3 & -5 \\ \hline -6 & -3 & -9 & -3 \\ \hline \end{array} \][/tex]
