Answer :

GinnyAnswer
Let's analyze the given matrix and find the value represented by the question mark (?). Here's the matrix:

[tex]\[ \begin{array}{cccc} -4 & -6 & -9 & -6 \\ ? & 7 & 4 & -4 \\ 9 & 3 & 2 & 6 \\ 3 & -4 & 8 & -6 \end{array} \][/tex]

First, we find the sum of each row that has no missing values.

### Step 1: Calculate the sum of each complete row

1. First row:

[tex]\[ -4 + (-6) + (-9) + (-6) = -25 \][/tex]

2. Third row:

[tex]\[ 9 + 3 + 2 + 6 = 20 \][/tex]

3. Fourth row:

[tex]\[ 3 + (-4) + 8 + (-6) = 3 - 4 + 8 - 6 = 1 \][/tex]

Therefore, the sums of the rows are:

[tex]\[ \text{Row Sums} = [-25, 20, 1] \][/tex]

### Step 2: Calculate the average sum of the complete rows

To find an average sum for the given rows, we add the row sums and divide by the number of rows:

[tex]\[ \text{Average Sum} = \frac{-25 + 20 + 1}{3} = \frac{-4}{3} = -1.3333 \][/tex]

### Step 3: Calculate the sum of the incomplete row (without the missing value)

For the second row, we have:

[tex]\[ 7 + 4 + (-4) = 7 \][/tex]

### Step 4: Determine the missing value

We need to find a value for [tex]\( ? \)[/tex] that, when added to 7, gives us a total that brings the row sum closer to the average sum of [tex]\(-1.3333\)[/tex]. Therefore:

[tex]\[ ? + 7 = -1.3333 \][/tex]

Solving for [tex]\( ? \)[/tex]:

[tex]\[ ? = -1.3333 - 7 = -8.3333 \][/tex]

Thus, the value replacing the question mark [tex]\( ? \)[/tex] is approximately:

[tex]\[ -8.3333 \][/tex]