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Find the transpose of the matrix. 84 -4 0 -7 7 4 8 0-4 7 -7 4 0 7 -4 -7 8 8 -4 -7 [849] 0 7 -7 7 H -4 0 84

Find the transpose of the matrix. 84 -4 0 -7 7 4 8 0-4 7 -7 4 0 7 -4 -7 8 8 -4 -7 [849] 0 7 -7 7 H -4 0 84

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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**Problem: Find the transpose of the matrix.** Given Matrix: \[ \begin{bmatrix} 8 & 4 \\ -4 & 0 \\ -7 & 7 \\ \end{bmatrix} \] **Options:** 1. \[ \begin{bmatrix} 4 & 8 \\ 0 & -4 \\ 7 & -7 \\ \end{bmatrix} \] 2. \[ \begin{bmatrix} 4 & 0 & 7 \\ 8 & -4 & -7 \\ \end{bmatrix} \] 3. \[ \begin{bmatrix} 8 & -4 & -7 \\ 4 & 0 & 7 \\ \end{bmatrix} \] 4. \[ \begin{bmatrix} -7 & 7 \\ -4 & 0 \\ 8 & 4 \\ \end{bmatrix} \] **Explanation:** The transpose of a matrix is formed by swapping the rows and columns. For the given matrix: - Row 1: \([8, 4]\) becomes Column 1: \([8, -4, -7]\) - Row 2: \([-4, 0]\) becomes Column 2: \([4, 0, 7]\) Therefore, the correct transpose is Option 3: \[ \begin{bmatrix} 8 & -4 & -7 \\ 4 & 0 & 7 \\ \end{bmatrix} \]
Transcribed Image Text:**Problem: Find the transpose of the matrix.** Given Matrix: \[ \begin{bmatrix} 8 & 4 \\ -4 & 0 \\ -7 & 7 \\ \end{bmatrix} \] **Options:** 1. \[ \begin{bmatrix} 4 & 8 \\ 0 & -4 \\ 7 & -7 \\ \end{bmatrix} \] 2. \[ \begin{bmatrix} 4 & 0 & 7 \\ 8 & -4 & -7 \\ \end{bmatrix} \] 3. \[ \begin{bmatrix} 8 & -4 & -7 \\ 4 & 0 & 7 \\ \end{bmatrix} \] 4. \[ \begin{bmatrix} -7 & 7 \\ -4 & 0 \\ 8 & 4 \\ \end{bmatrix} \] **Explanation:** The transpose of a matrix is formed by swapping the rows and columns. For the given matrix: - Row 1: \([8, 4]\) becomes Column 1: \([8, -4, -7]\) - Row 2: \([-4, 0]\) becomes Column 2: \([4, 0, 7]\) Therefore, the correct transpose is Option 3: \[ \begin{bmatrix} 8 & -4 & -7 \\ 4 & 0 & 7 \\ \end{bmatrix} \]
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