Q30E Find the elementary row operatio... [FREE SOLUTION]

91影视

Linear Algebra and its Applications

David C. Lay, Steven R. Lay and Judi J. McDonald

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 483 pages

ISBN: 978-03219822384

Chapter 1: Q30E (page 1)

Find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.
30.$\left[ {\begin{array}{{20}{c}}1&3&{ - 4}\\0&{ - 2}&6\\0&{ - 5}&9\end{array}} \right]$, $\left[ {\begin{array}{{20}{c}}1&3&{ - 4}\\0&1&{ - 3}\\0&{ - 5}&9\end{array}} \right]$

Short Answer

Expert verified

The row operation to transform the first matrix into the second is the multiplication of row two by $ - \frac{1}{2}$, i.e., ${R_2} \to - \frac{1}{2}{R_2}$ in the first matrix. And the reverse row operation is the multiplication of row two by $ - 2$, i.e., ${R_2} \to - 2{R_2}$ in the second matrix.

Step by step solution

Rewrite the given matrices

The given matrices are:

$\left[ {\begin{array}{*{20}{c}}1&3&{ - 4}\\0&{ - 2}&6\\0&{ - 5}&9\end{array}} \right]$, $\left[ {\begin{array}{*{20}{c}}1&3&{ - 4}\\0&1&{ - 3}\\0&{ - 5}&9\end{array}} \right]$

Apply the elementary row operation

A basic principle states that row operations do not affect the solution set of a linear system.

Perform an elementaryrow operation.

Multiply row two by $ - \frac{1}{2}$ in the first matrix, $\left[ {\begin{array}{*{20}{c}}1&3&{ - 4}\\0&{ - 2}&6\\0&{ - 5}&9\end{array}} \right]$, and transform it to the second matrix, $\left[ {\begin{array}{*{20}{c}}1&3&{ - 4}\\0&1&{ - 3}\\0&{ - 5}&9\end{array}} \right]$.

Apply the elementary row operation

A basic principle states that row operations do not affect the solution set of a linear system.

Perform an elementary row operation.

Multiply row two by $ - 2$ in the second matrix, $\left[ {\begin{array}{*{20}{c}}1&3&{ - 4}\\0&1&{ - 3}\\0&{ - 5}&9\end{array}} \right]$, and transform it to the first matrix, $\left[ {\begin{array}{*{20}{c}}1&3&{ - 4}\\0&{ - 2}&6\\0&{ - 5}&9\end{array}} \right]$.

Thus, the row operation is the multiplication of row two by $ - \frac{1}{2}$ in the first matrix. And the reverse row operation is the multiplication of row two by $ - 2$ in the second matrix.