3 * [[1, 2], [3, - 1]] + [[2p, - 2], [- 4, 5]] = [[- 1, 2], [1, 1]] * [[1, 0], [4, 2]] Maka nilai p adalah

Let's break down the equation step-by-step to find the value of \( p \):

1. **Matrix Multiplication and Scalar Multiplication:**
   - First, compute the scalar multiplication of the matrix \( 3 \times \begin{bmatrix} 1 & 2 \\ 3 & -1 \end{bmatrix} \):
     \[
     3 \times \begin{bmatrix} 1 & 2 \\ 3 & -1 \end{bmatrix} = \begin{bmatrix} 3 \times 1 & 3 \times 2 \\ 3 \times 3 & 3 \times (-1) \end{bmatrix} = \begin{bmatrix} 3 & 6 \\ 9 & -3 \end{bmatrix}.
     \]

   - Next, perform the matrix multiplication of \( \begin{bmatrix} -1 & 2 \\ 1 & 1 \end{bmatrix} \) and \( \begin{bmatrix} 1 & 0 \\ 4 & 2 \end{bmatrix} \):
     \[
     \begin{bmatrix} -1 & 2 \\ 1 & 1 \end{bmatrix} \times \begin{bmatrix} 1 & 0 \\ 4 & 2 \end{bmatrix} = \begin{bmatrix} (-1 \times 1) + (2 \times 4) & (-1 \times 0) + (2 \times 2) \\ (1 \times 1) + (1 \times 4) & (1 \times 0) + (1 \times 2) \end{bmatrix}.
     \]

   Simplifying this:
     \[
     \begin{bmatrix} -1 + 8 & 0 + 4 \\ 1 + 4 & 0 + 2 \end{bmatrix} = \begin{bmatrix} 7 & 4 \\ 5 & 2 \end{bmatrix}.
     \]

2. **Set Up the Equation:**
   - We are given the equation:
     \[
     \begin{bmatrix} 3 & 6 \\ 9 & -3 \end{bmatrix} + \begin{bmatrix} 2p & -2 \\ -4 & 5 \end{bmatrix} = \begin{bmatrix} 7 & 4 \\ 5 & 2 \end{bmatrix}.
     \]

3. **Combine the Matrices:**
   - Add the matrices on the left-hand side:
     \[
     \begin{bmatrix} 3 + 2p & 6 + (-2) \\ 9 + (-4) & -3 + 5 \end{bmatrix} = \begin{bmatrix} 3 + 2p & 6 - 2 \\ 9 - 4 & -3 + 5 \end{bmatrix}.
     \]

   Simplifying this:
     \[
     \begin{bmatrix} 3 + 2p & 4 \\ 5 & 2 \end{bmatrix}.
     \]

4. **Set Up and Solve for \( p \):**
   - Now equate this to the right-hand side matrix:
     \[
     \begin{bmatrix} 3 + 2p & 4 \\ 5 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 4 \\ 5 & 2 \end{bmatrix}.
     \]

   - From the first element of the matrices, we have:
     \[
     3 + 2p = 7.
     \]

   - Solve for \( p \):
     \[
     2p = 7 - 3,
     \]
     \[
     2p = 4,
     \]
     \[
     p = \frac{4}{2} = 2.
     \]

So, the value of \( p \) is \( 2 \).

Do you want more details or have any questions?

### Related Questions:
1. How do you multiply two matrices?
2. What is scalar multiplication of a matrix?
3. What are the properties of matrix addition?
4. How can matrices be used to solve systems of linear equations?
5. What are the conditions for two matrices to be equal?

**Tip:** When adding or equating matrices, make sure each corresponding element matches to ensure the equation holds true.

3 * [[1, 2], [3, -1]] + [[2p, -2], [-4, 5]] = [[-1, 2], [1, 1]] * [[1, 0], [4, 2]] Maka nilai p adalah

This detailed solution walks through solving a matrix equation to find the value of p, using scalar multiplication, matrix multiplication, and matrix addition. Suitable for high school 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