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5. Perform the row operation R, and replace R, on the following matrix. 7 500 30 03 0 7 3 7 0 0 32 0. 3 2

5. Perform the row operation R, and replace R, on the following matrix. 7 500 30 03 0 7 3 7 0 0 32 0. 3 2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Matrix Row Operation Example:** In this exercise, you are required to perform a row operation on a matrix. The operation to be executed is: \[ \frac{1}{5} R_1 \quad \text{and replace } R_1 \] **Starting Matrix:** \[ \begin{bmatrix} 5 & 0 & 0 & 30 \\ 0 & 3 & 0 & 7 \\ 0 & 0 & 3 & 2 \\ \end{bmatrix} \] **Operation Explained:** The operation involves multiplying every element of the first row (\(R_1\)) by \(\frac{1}{5}\): 1. The first element of \(R_1\) is \(5\): \(\frac{1}{5} \times 5 = 1\) 2. The second element is \(0\): \(\frac{1}{5} \times 0 = 0\) 3. The third element is \(0\): \(\frac{1}{5} \times 0 = 0\) 4. The fourth element is \(30\): \(\frac{1}{5} \times 30 = 6\) **Transformed Matrix:** \[ \begin{bmatrix} 1 & 0 & 0 & 6 \\ 0 & 3 & 0 & 7 \\ 0 & 0 & 3 & 2 \\ \end{bmatrix} \] This operation simplifies the first row, preparing the matrix for further manipulations or solution processes.
Transcribed Image Text:**Matrix Row Operation Example:** In this exercise, you are required to perform a row operation on a matrix. The operation to be executed is: \[ \frac{1}{5} R_1 \quad \text{and replace } R_1 \] **Starting Matrix:** \[ \begin{bmatrix} 5 & 0 & 0 & 30 \\ 0 & 3 & 0 & 7 \\ 0 & 0 & 3 & 2 \\ \end{bmatrix} \] **Operation Explained:** The operation involves multiplying every element of the first row (\(R_1\)) by \(\frac{1}{5}\): 1. The first element of \(R_1\) is \(5\): \(\frac{1}{5} \times 5 = 1\) 2. The second element is \(0\): \(\frac{1}{5} \times 0 = 0\) 3. The third element is \(0\): \(\frac{1}{5} \times 0 = 0\) 4. The fourth element is \(30\): \(\frac{1}{5} \times 30 = 6\) **Transformed Matrix:** \[ \begin{bmatrix} 1 & 0 & 0 & 6 \\ 0 & 3 & 0 & 7 \\ 0 & 0 & 3 & 2 \\ \end{bmatrix} \] This operation simplifies the first row, preparing the matrix for further manipulations or solution processes.
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