https://file.aiquickdraw.com/mathbot/file/1727091764580frs3bmb9.jpg

Let's analyze the problem shown in the image.

We are given two matrices, \( A \) and \( B \), and we know that:

\[
A = \begin{pmatrix} 3a & 1 & 6 \\ 1 & 5 & -2b \\ 6 & 2c & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 12 & 1 & 6 \\ 1 & 5 & -2a \\ 6 & 6 & 4 \end{pmatrix}
\]

We are also given that \( A = B \). Therefore, corresponding elements of both matrices must be equal.

By comparing corresponding elements of matrices \( A \) and \( B \):

1. In the first row, first column: 
   \[
   3a = 12 \quad \Rightarrow \quad a = \frac{12}{3} = 4
   \]

2. In the second row, third column:
   \[
   -2b = -2a \quad \Rightarrow \quad -2b = -2(4) \quad \Rightarrow \quad b = 4
   \]

3. In the third row, second column:
   \[
   2c = 6 \quad \Rightarrow \quad c = \frac{6}{2} = 3
   \]

Now that we have the values of \( a \), \( b \), and \( c \), the final step is to compute \( a + b + c \):

\[
a + b + c = 4 + 4 + 3 = 11
\]

Thus, the answer is \( a + b + c = 11 \).

---

Do you need further clarifications? Here are 5 related questions to practice:

1. How would the solution change if the matrix \( A \) had a different form?
2. What if the matrix \( A \) was not equal to \( B \), how would you solve for \( a \), \( b \), and \( c \)?
3. Can you generalize the method for solving for unknowns in two equal matrices?
4. How do you handle matrices of larger dimensions when comparing elements?
5. What are the properties of matrix equality?

**Tip:** When comparing matrices element-wise, ensure that both matrices have the same dimensions before proceeding with the comparison.

Diketahui matriks A = [[3a, 1, 6], [1, 5, -2b], [6, 2c, 4]], dan B = [[12, 1, 6], [1, 5, -2a], [6, 6, 4]]. Jika A = B, maka a + b + c = ...

Solve the matrix equality problem A = [[3a, 1, 6], [1, 5, -2b], [6, 2c, 4]] and B = [[12, 1, 6], [1, 5, -2a], [6, 6, 4]]. Find the values of a, b, and c that satisfy the equation, and calculate a + b + c. This algebraic problem explores matrix equality and element-wise comparison, suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation