Alright, let's solve this problem step-by-step to find the missing value in the matrix:
[tex]\[
\begin{array}{llll}
9 & 1 & 6 & 4 \\
4 & 5 & 7 & 2 \\
5 & 8 & 8 & 5 \\
1 & 3 & 5 & ?
\end{array}
\][/tex]
### Step 1: Analyze the Given Rows
First, let's examine each row and see if there's a pattern.
#### Row 1:
[tex]\[ 9 + 1 + 6 = 16 \][/tex]
Subtracting the fourth element:
[tex]\[ 16 - 4 = 12 \][/tex]
#### Row 2:
[tex]\[ 4 + 5 + 7 = 16 \][/tex]
Subtracting the fourth element:
[tex]\[ 16 - 2 = 14 \][/tex]
#### Row 3:
[tex]\[ 5 + 8 + 8 = 21 \][/tex]
Subtracting the fourth element:
[tex]\[ 21 - 5 = 16 \][/tex]
### Step 2: Identify the Pattern
We notice that the sum of the first three elements subtracted by the fourth element does not match a consistent pattern in terms of outcome. Let's check the possible consistency within the rows themselves.
### Step 3: Perform Analysis on the Fourth Row
For the fourth row:
[tex]\[ 1 + 3 + 5 = 9 \][/tex]
We need this to meet a certain condition or consistency noted from the previous rows.
From our observations from rows 1 through 3:
- For Row 1, [tex]\( 16 - 4 = 12 \)[/tex]
- For Row 2, [tex]\( 16 - 2 = 14 \)[/tex]
- For Row 3, [tex]\( 21 - 5 = 16 \)[/tex]
A common thread appears when we check row 4. We have:
[tex]\[ 1 + 3 + 5 = 9 \][/tex]
If there was a consistent pattern, like aiming for a consistent post-subtraction result around 16, we'd need to establish continuity:
[tex]\[ 1 + 3 + 5 + ? = 16\][/tex]
Thus:
[tex]\[ 9 + ? = 16 \Rightarrow ? = 7 \][/tex]
So, the missing value in the fourth row is:
[tex]\[ \boxed{7} \][/tex]
