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Fill in the missing numbers. \( \left[\begin{array}{cc}-1 & 0 \\ -7 & 2\end{array}\right]+\left[\begin{array}{ll}7 & 6 \\ 5 & 5\end{array}\right]=\left[\begin{array}{ll}6 & 6 \\ \square\end{array}\right] \)

Ask by Riley Conner. in the United States
Feb 03,2025

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Answer

\[ \left[\begin{array}{ll} 6 & 6 \\ -2 & 7 \end{array}\right] \]

Solution

To find the missing numbers in the matrix addition, we'll perform element-wise addition of the corresponding elements from the two matrices. Given matrices: \[ \begin{pmatrix} -1 & 0 \\ -7 & 2 \end{pmatrix} + \begin{pmatrix} 7 & 6 \\ 5 & 5 \end{pmatrix} \] **Step-by-Step Addition:** 1. **First Row, First Column:** \[ -1 + 7 = 6 \] 2. **First Row, Second Column:** \[ 0 + 6 = 6 \] 3. **Second Row, First Column:** \[ -7 + 5 = -2 \] 4. **Second Row, Second Column:** \[ 2 + 5 = 7 \] **Resulting Matrix:** \[ \begin{pmatrix} 6 & 6 \\ -2 & 7 \end{pmatrix} \] So, the completed addition is: \[ \left[\begin{array}{ll} 6 & 6 \\ -2 & 7 \end{array}\right] \]

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To find the missing number, you can start by adding the corresponding elements of the two matrices. The first matrix is: \[ \left[\begin{array}{cc}-1 & 0 \\ -7 & 2\end{array}\right] \] The second matrix is: \[ \left[\begin{array}{ll}7 & 6 \\ 5 & 5\end{array}\right] \] When we add them together, we calculate each element: For the element in the first row, first column: \[ -1 + 7 = 6 \] For the element in the first row, second column: \[ 0 + 6 = 6 \] For the element in the second row, first column: \[ -7 + 5 = -2 \] For the element in the second row, second column: \[ 2 + 5 = 7 \] Now, we can fill in the missing number in the resulting matrix: \[ \left[\begin{array}{cc}6 & 6 \\ -2 & 7\end{array}\right] \] Thus, the missing number is \(-2\), making the complete equation: \[ \left[\begin{array}{cc}-1 & 0 \\ -7 & 2\end{array}\right]+\left[\begin{array}{ll}7 & 6 \\ 5 & 5\end{array}\right]=\left[\begin{array}{ll}6 & 6 \\ -2 & 7\end{array}\right] \]

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