https://file.aiquickdraw.com/mathbot/file/17272654015929vcksok8.jpg

You've uploaded a problem set containing matrix-related questions. I will help with the first question and provide detailed solutions. The first question asks:

**1. Diketahui:**
\[ A = \begin{bmatrix} 3 & -4 \\ 2 & 1 \end{bmatrix}, B = \begin{bmatrix} -3 & 5 \\ -2 & 1 \end{bmatrix}, C = \begin{bmatrix} 5 & -2 \\ -4 & -1 \end{bmatrix} \]

Find:
\[ 3A^T - B + 2C \]

### Steps to solve:

1. **Transpose of A (A^T):**
   \[
   A^T = \begin{bmatrix} 3 & 2 \\ -4 & 1 \end{bmatrix}
   \]
   
2. **Multiply \( A^T \) by 3:**
   \[
   3A^T = 3 \times \begin{bmatrix} 3 & 2 \\ -4 & 1 \end{bmatrix} = \begin{bmatrix} 9 & 6 \\ -12 & 3 \end{bmatrix}
   \]

3. **Multiply C by 2:**
   \[
   2C = 2 \times \begin{bmatrix} 5 & -2 \\ -4 & -1 \end{bmatrix} = \begin{bmatrix} 10 & -4 \\ -8 & -2 \end{bmatrix}
   \]

4. **Now, compute \( 3A^T - B + 2C \):**
   \[
   B = \begin{bmatrix} -3 & 5 \\ -2 & 1 \end{bmatrix}
   \]

   Perform the subtraction and addition:
   \[
   3A^T - B = \begin{bmatrix} 9 & 6 \\ -12 & 3 \end{bmatrix} - \begin{bmatrix} -3 & 5 \\ -2 & 1 \end{bmatrix} = \begin{bmatrix} 12 & 1 \\ -10 & 2 \end{bmatrix}
   \]
   Then:
   \[
   3A^T - B + 2C = \begin{bmatrix} 12 & 1 \\ -10 & 2 \end{bmatrix} + \begin{bmatrix} 10 & -4 \\ -8 & -2 \end{bmatrix} = \begin{bmatrix} 22 & -3 \\ -18 & 0 \end{bmatrix}
   \]

The final result is:
\[
3A^T - B + 2C = \begin{bmatrix} 22 & -3 \\ -18 & 0 \end{bmatrix}
\]

Would you like a detailed explanation for the next question or clarification on this one?

Here are 5 related questions you might explore:
1. How do you find the inverse of a 2x2 matrix?
2. What are the properties of matrix addition and scalar multiplication?
3. How does transposing a matrix affect its properties?
4. Can every matrix be inverted? If not, why?
5. What is the geometric interpretation of matrix multiplication?

**Tip:** Always check if matrices are compatible in size before performing operations like addition and multiplication.

Diketahui A = [3, -4; 2, 1], B = [-3, 5; -2, 1], C = [5, -2; -4, -1]. Tentukan 3A^T - B + 2C !

Learn how to solve the matrix equation 3A^T - B + 2C. This problem involves matrix transposition, scalar multiplication, and matrix addition and subtraction, suitable for students in 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