Q1.2 29E Is there a sequence of elementar... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 1: Q1.2 29E (page 19)

Is there a sequence of elementary row operations that transforms
$[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}]$ into $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ ?

Short Answer

Expert verified

No, there is not any sequence of operation that transform $[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}]$ into $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ .

Step by step solution

Row operations for changing the matrix

We have given a matrix for transforming the matrix we will follow the following operations.

$[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}] R_{2} 鈫� R_{2} - 4 R_{1} R_{3} 鈫� R_{3} - 7 R_{1} ~ [\begin{matrix} 1 & 2 & 3 \\ 0 & - 3 & - 6 \\ 0 & - 6 & - 12 \end{matrix}] R_{2} 鈫� \frac{1}{- 3} R_{2} R_{3} 鈫� \frac{1}{- 6} R_{3} ~ [\begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 1 & 2 \end{matrix}]$

Solving matrix

Now proceeding further with more sequence of operation

$R_{1} 鈫� R_{1} - 2 R_{2} R_{3} 鈫� R_{3} - R_{2}$

Using these above operations we get,

$~ [\begin{matrix} 1 & 0 & - 1 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{matrix}] 鈮� [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{matrix}]$

Hence there is not any sequence of operation that transform $[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}]$ into $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ .

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91影视

Is there a sequence of elementary row operations that transforms
$[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}]$ into $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ ?

Short Answer

Step by step solution

Row operations for changing the matrix

Solving matrix

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91影视

Is there a sequence of elementary row operations that transforms[123456789]into [100010001]?

Short Answer

Step by step solution

Row operations for changing the matrix

Solving matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Is there a sequence of elementary row operations that transforms
$[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}]$ into $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ ?