https://file.aiquickdraw.com/mathbot/file/1726038948441w2oifayh.jpg

We are given three matrices \( A \), \( B \), and \( C \), with the equation \( A + B = C \), and asked to determine the values of \( p \), \( q \), and \( r \).

Let's write the matrices out clearly:

\[
A = \begin{pmatrix} 
2p & 2 & -3a \\
4 & -1 & -4 \\
r & q & -2 
\end{pmatrix}, \quad
B = \begin{pmatrix} 
-p & -7 & q \\
-5 & 4 & r \\
-5 & 4 & 7 
\end{pmatrix}, \quad
C = \begin{pmatrix} 
2 & -5 & 6 \\
-1 & 4 & -2 \\
-3 & 1 & 5 
\end{pmatrix}
\]

We know that \( A + B = C \). Therefore, for each element, we have the following system of equations by comparing corresponding elements:

### First row:
\[
(2p) + (-p) = 2 \quad \Rightarrow \quad p = 2
\]
\[
2 + (-7) = -5 \quad \text{(This is already correct)}
\]
\[
-3a + q = 6
\]

### Second row:
\[
4 + (-5) = -1 \quad \text{(This is correct)}
\]
\[
-1 + 4 = 4 \quad \text{(This is correct)}
\]
\[
-4 + r = -2 \quad \Rightarrow \quad r = 2
\]

### Third row:
\[
r + (-5) = -3 \quad \Rightarrow \quad r = 2 \quad \text{(This is consistent)}
\]
\[
q + 4 = 1 \quad \Rightarrow \quad q = -3
\]
\[
-2 + 7 = 5 \quad \text{(This is correct)}
\]

Thus, the values are:
\[
p = 2, \quad q = -3, \quad r = 2
\]

The correct answer is option **D**: 2, -3, and 2.

Would you like more details or have further questions?

Here are some related questions:
1. What is the definition of matrix addition?
2. How do we solve systems of linear equations?
3. How are matrix dimensions important when adding matrices?
4. What happens when matrices have unequal dimensions?
5. How can matrix equations be solved using Gaussian elimination?

**Tip:** Always ensure that matrices are of the same dimension when performing addition.

Diketahui matriks A dan B, jika A + B = C, maka nilai p, q, dan r berturut-turut adalah?

Solve a matrix addition problem where A + B = C, and find the values of p, q, and r. This exercise involves basic matrix operations and systems of linear equations. Suitable for high school or first-year college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation