Questions: Apply the indicated operation to the matrix, then choose the correct matrix. [3 1 -5; 0 -2 4] [-5 1 3; 4 -2 0] [0 4 -2; 3 -5 1] [4 -2 0; -5 1 3]

Apply the indicated operation to the matrix, then choose the correct matrix. [3 1 -5; 0 -2 4] [-5 1 3; 4 -2 0] [0 4 -2; 3 -5 1] [4 -2 0; -5 1 3]
Transcript text: 6) Apply the indicated operation to the matrix, then choose the correct matrix. $\left[\begin{array}{ccc}3 & 1 & -5 \\ 0 & -2 & 4\end{array}\right]$ $\left[\begin{array}{ccc}-5 & 1 & 3 \\ 4 & -2 & 0\end{array}\right]$ $\left[\begin{array}{ccc}0 & 4 & -2 \\ 3 & -5 & 1\end{array}\right]$ $\left[\begin{array}{ccc}4 & -2 & 0 \\ -5 & 1 & 3\end{array}\right]$
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Solution

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Solution Steps

Solution Approach

To solve this problem, we need to determine the indicated operation to be applied to the given matrix. Since the operation is not specified in the question, we will assume it is a common matrix operation such as addition, subtraction, or multiplication. For this example, let's assume we are performing matrix addition. We will add the given matrix to each of the provided matrices and check which one matches the result.

Step 1: Given Matrices

We have the following matrices: \[ A = \begin{bmatrix} 3 & 1 & -5 \\ 0 & -2 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} -5 & 1 & 3 \\ 4 & -2 & 0 \end{bmatrix}, \quad C = \begin{bmatrix} 0 & 4 & -2 \\ 3 & -5 & 1 \end{bmatrix}, \quad D = \begin{bmatrix} 4 & -2 & 0 \\ -5 & 1 & 3 \end{bmatrix} \]

Step 2: Matrix Addition

We will perform the addition of matrix \( A \) with each of the provided matrices \( B \), \( C \), and \( D \).

  1. Addition with \( B \): \[ A + B = \begin{bmatrix} 3 & 1 & -5 \\ 0 & -2 & 4 \end{bmatrix} + \begin{bmatrix} -5 & 1 & 3 \\ 4 & -2 & 0 \end{bmatrix} = \begin{bmatrix} -2 & 2 & -2 \\ 4 & -4 & 4 \end{bmatrix} \]

  2. Addition with \( C \): \[ A + C = \begin{bmatrix} 3 & 1 & -5 \\ 0 & -2 & 4 \end{bmatrix} + \begin{bmatrix} 0 & 4 & -2 \\ 3 & -5 & 1 \end{bmatrix} = \begin{bmatrix} 3 & 5 & -7 \\ 3 & -7 & 5 \end{bmatrix} \]

  3. Addition with \( D \): \[ A + D = \begin{bmatrix} 3 & 1 & -5 \\ 0 & -2 & 4 \end{bmatrix} + \begin{bmatrix} 4 & -2 & 0 \\ -5 & 1 & 3 \end{bmatrix} = \begin{bmatrix} 7 & -1 & -5 \\ -5 & -1 & 7 \end{bmatrix} \]

Step 3: Results Comparison

The results of the additions are:

  • \( A + B = \begin{bmatrix} -2 & 2 & -2 \\ 4 & -4 & 4 \end{bmatrix} \)
  • \( A + C = \begin{bmatrix} 3 & 5 & -7 \\ 3 & -7 & 5 \end{bmatrix} \)
  • \( A + D = \begin{bmatrix} 7 & -1 & -5 \\ -5 & -1 & 7 \end{bmatrix} \)

None of the resulting matrices match the original matrices \( B \), \( C \), or \( D \) directly. However, we can conclude that the operation performed does not yield any of the provided matrices as a result.

Final Answer

Since none of the resulting matrices match the provided options, we conclude that the correct matrix is not among the choices given. Thus, the answer is: \[ \boxed{\text{No correct matrix found}} \]

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