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To find the value of \( K \) in the equation involving matrices, we need to follow matrix equality principles. The equation given is:

\[
\begin{bmatrix}
16 & 8 & 26 \\
6 & 3 & 9 \\
2 & 1 & 4
\end{bmatrix}
= 
\begin{bmatrix}
1 & 2 & 5 \\
2 & K & 0 \\
7 & 14 & 9
\end{bmatrix}
\]

For two matrices to be equal, corresponding elements in both matrices must be equal. So, we equate the elements at the same positions in the matrices.

Let's focus on the element in the second row and second column (position (2,2)):

From the left matrix: \( 3 \)
From the right matrix: \( K \)

Therefore, \( K = 3 \).

So, the value of \( K \) is:

\[
K = 3
\]

Let me know if you need further clarification!

Here are 5 related questions:
1. How do you add two matrices together?
2. What are the conditions for two matrices to be equal?
3. Can two matrices of different dimensions be compared?
4. What is the result of multiplying a scalar with a matrix?
5. How is matrix multiplication different from regular multiplication?

**Tip**: When working with matrices, always ensure their dimensions are compatible before performing operations like addition or multiplication.

If [16 8 26; 6 3 9; 2 1 4] = [1 2 5; 2 K 0; 7 14 9], find the value of K.

Learn how to find the value of K in a matrix equation by applying the matrix equality theorem. This problem is ideal for students in Grades 8-10 and covers key concepts in linear algebra, including matrix operations and equality.

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