Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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The image shows a handwritten mathematical expression involving matrix operations. The matrix is defined as follows: Let \( A = \begin{bmatrix} 3 & 5 \\ 0 & 2 \\ 1 & 4 \\ 2 & 8 \end{bmatrix} \). The task is to find the product \( A^T A \), where \( A^T \) denotes the transpose of matrix \( A \). - **Matrix \( A \):** A 4x2 matrix with the elements arranged as described above. - **Goal:** Calculate the product of the transpose of \( A \) and \( A \) itself. To solve this, follow these steps: 1. **Transpose \( A \):** The transpose of a matrix is obtained by swapping its rows and columns. 2. **Multiply \( A^T \) and \( A \):** Recall that the number of columns in the first matrix must match the number of rows in the second matrix when performing matrix multiplication. This is a common exercise in linear algebra involving matrix operations and product calculations.
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Transcribed Image Text:The image shows a handwritten mathematical expression involving matrix operations. The matrix is defined as follows: Let \( A = \begin{bmatrix} 3 & 5 \\ 0 & 2 \\ 1 & 4 \\ 2 & 8 \end{bmatrix} \). The task is to find the product \( A^T A \), where \( A^T \) denotes the transpose of matrix \( A \). - **Matrix \( A \):** A 4x2 matrix with the elements arranged as described above. - **Goal:** Calculate the product of the transpose of \( A \) and \( A \) itself. To solve this, follow these steps: 1. **Transpose \( A \):** The transpose of a matrix is obtained by swapping its rows and columns. 2. **Multiply \( A^T \) and \( A \):** Recall that the number of columns in the first matrix must match the number of rows in the second matrix when performing matrix multiplication. This is a common exercise in linear algebra involving matrix operations and product calculations.
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