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Write as a single matrix: ((-1,2,3))((-2...

Write as a single matrix: `((-1,2,3))((-2,-1,5),(0,-1,4),(7,0,5))-2((4,-5,-7))`

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To solve the problem, we will follow these steps: ### Step 1: Define the matrices Let \( A = (-1, 2, 3) \) be a row matrix and \( B = \begin{pmatrix} -2 & -1 & 5 \\ 0 & -1 & 4 \\ 7 & 0 & 5 \end{pmatrix} \) be a 3x3 matrix. We also have a row matrix \( C = (4, -5, -7) \). ### Step 2: Multiply matrix A with matrix B To find the product \( A \times B \), we compute the following: \[ A \times B = (-1, 2, 3) \begin{pmatrix} -2 & -1 & 5 \\ 0 & -1 & 4 \\ 7 & 0 & 5 \end{pmatrix} \] Calculating each element of the resulting matrix: 1. First column: \[ -1 \times -2 + 2 \times 0 + 3 \times 7 = 2 + 0 + 21 = 23 \] 2. Second column: \[ -1 \times -1 + 2 \times -1 + 3 \times 0 = 1 - 2 + 0 = -1 \] 3. Third column: \[ -1 \times 5 + 2 \times 4 + 3 \times 5 = -5 + 8 + 15 = 18 \] Thus, we have: \[ A \times B = (23, -1, 18) \] ### Step 3: Multiply the result by -2 times matrix C Now we need to compute \( -2 \times C \): \[ -2 \times (4, -5, -7) = (-8, 10, 14) \] ### Step 4: Add the two results Now we add the results from Step 2 and Step 3: \[ (23, -1, 18) + (-8, 10, 14) \] Calculating each element: 1. First element: \[ 23 - 8 = 15 \] 2. Second element: \[ -1 + 10 = 9 \] 3. Third element: \[ 18 + 14 = 32 \] Thus, the final result is: \[ (15, 9, 32) \] ### Final Answer The single matrix representation is: \[ \boxed{(15, 9, 32)} \] ---
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