Problem Description:
The image shows a 3x3 matrix with numerical values. The task is to determine the missing value in the matrix, represented by the red question mark (?).
The matrix is as follows:
\[
\begin{bmatrix}
4 & 2 & 6 \\
5 & 4 & 9 \\
9 & 6 & ?
\end{bmatrix}
\]
Solution Approach:
To solve this problem, we need to identify a pattern or rule that governs the relationship between the numbers in the matrix. Let's analyze the matrix step by step.
#### Step 1: Examine Rows and Columns
We will check if there is a consistent mathematical relationship between the numbers in each row or column.
##### Row Analysis:
-
First Row: \(4, 2, 6\)
- Sum: \(4 + 2 = 6\)
-
Second Row: \(5, 4, 9\)
- Sum: \(5 + 4 = 9\)
-
Third Row: \(9, 6, ?\)
- Sum: \(9 + 6 = 15\)
From this analysis, it appears that the sum of the first two numbers in each row equals the third number.
#### Step 2: Verify the Pattern
Let's verify if this pattern holds consistently:
- In the first row: \(4 + 2 = 6\) (correct)
- In the second row: \(5 + 4 = 9\) (correct)
- In the third row: \(9 + 6 = 15\) (correct)
#### Step 3: Determine the Missing Value
Based on the observed pattern, the missing value in the third row should be the sum of the first two numbers in that row:
\[
9 + 6 = 15
\]
Final Answer:
The missing value in the matrix is \(\boxed{15}\).
Thus, the completed matrix is:
\[
\begin{bmatrix}
4 & 2 & 6 \\
5 & 4 & 9 \\
9 & 6 & 15
\end{bmatrix}
\]
Parent Tip: Review the logic above to help your child master the concept of printable iq test for 5 year olds.
