Learning Materials
Features
Discover
Chapter 5: Problem 220
Determine the parity of \(\sigma=542163\).
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
1\. Which of the following matrices are in reduced-row chelon form? \(\begin{array}{lllllll}\text { (a) } & \mid 1 & 0 & 0 & \text { (b) } & \mid 0 & 1 & 0 \\ & \mid 0 & 0 & 0 \mid & & 1 & 0 & 0 \\ & \mid 0 & 0 & 1 & & 0 & 0 & 0\end{array}\) (c) \(\begin{array}{rrr}\mid 1 & 1 & 0 \\ & \mid 0 & 1 & 0 \\ & \mid 0 & 0 & 0\end{array} \mid\) (d) \(\begin{array}{lllll} & 11 & 2 & 0 & 3 & 0 \\ & 10 & 0 & 1 & 1 & 0 \\ & \mid 0 & 0 & 0 & 0 & 1 \\ & \mid 0 & 0 & 0 & 0 & 0\end{array}\) (e) \(\begin{array}{llll} & 1 & 0 & 0 & 5 \mid \\ & \mid 0 & 0 & 1 & 3 \mid \\\ & \mid 0 & 1 & 0 & 4\end{array}\) (f) \(\quad \begin{array}{cccc}1 & 0 & 3 & 1 \mid \\ & 0 & 1 & 2 & 4\end{array}\) 2\. Which of the following matrices are in row-echelon form? (a) \(\begin{array}{ccc}\mid 1 & 2 & 3 \\ & \mid 0 & 0 & 0 \\ & \mid 0 & 0 & 1\end{array}\) (b) \(\quad\left|\begin{array}{ccc}1 & -7 & 5 & 5 \mid \\ & \mid 0 & 1 & 3 & 2\end{array}\right|\) (c) \(\begin{array}{rrr} & \mid 1 & 1 & 0 \\ & \mid 0 & 1 & 0 \mid \\ & \mid 0 & 0 & 0\end{array} \mid\) (d) \(\begin{array}{rllll} & 1 & 3 & 0 & 2 & 0 \\ & 11 & 0 & 2 & 2 & 0 \\ & 10 & 0 & 0 & 0 & 1 \mid \\ & 10 & 0 & 0 & 0 & 0\end{array}\) (e) \(\begin{array}{rll} & \mid 2 & 3 & 4 \mid \\ & \mid 0 & 1 & 2 \mid \\ & \mid 0 & 0 & 3\end{array} \mid\) (f) \(\begin{array}{ccc} & \mid 0 & 0 & 0 \\ & \mid 0 & 0 & 0 \\ & \mid 0 & 0 & 0\end{array} \mid\)
Find the rank of the matrix A where: (i) \(\quad \begin{array}{rrrrrr} & \mid 1 & 3 & 1 & -2 & -3 \mid \\ & A=\mid 1 & 4 & 3 & -1 & -4 \mid \\ & \mid 2 & 3 & -4 & -7 & -3 \\ & \mid 3 & 8 & 1 & -7 & -8 \mid\end{array}\) (ii) \(\quad \begin{aligned}&\mid 1 & 2 & -3 \mid \\\&A= & \mid 2 & 1 & 0 \mid \\\&\mid-2 & -1 & 3 \\\&\mid-1 & 4 & -2\end{aligned} \mid\) (iii) \(\quad \begin{array}{rr}\mid 1 & 3 \mid \\ A=\mid & -2 \mid \\ \mid 5 & -1 \mid \\ \mid-2 & 3\end{array} \mid\)
Compute \(\mathrm{u} \cdot \mathrm{v}\) where i) \(\mathrm{u}=(2,-3,6) ; \mathrm{v}=(8,2,-3)\); ii) \(\mathrm{u}=(1,-8,0,5), \mathrm{v}=(3,6,4)\) iii) \(\mathrm{u}=(3,-5,2,1), \mathrm{v}=(4,1,-2,5)\)
\(\mathrm{A}=\mid \begin{array}{lll}1 & 1 \mid \text { and } \mathrm{P}=\mid 1 & 1 \mid \\ \mid \begin{array}{ll}0 & 1 \mid\end{array} & \mid 1 & -1 \mid \text { . }\end{array}\) (a) Find \(\mathrm{P}^{-1}\). (b) Find \(\mathrm{P}^{-1} \mathrm{AP}\). (c) Verify that, if \(\mathrm{B}\) is similar to \(\mathrm{A}\) then \(\mathrm{A}\) is similar to \(\mathrm{B}\). (d) Show that \(\mathrm{B}^{\mathrm{k}}=\mathrm{P}^{-1} \mathrm{~A}^{\mathrm{k} \mathrm{P}}\) if \(\mathrm{B}=\mathrm{P}^{-1}\) AP where \(\mathrm{k}\) is any positive integer.
Show that the following system has more than one solution. $$ \begin{aligned} 3 \mathrm{x}-\mathrm{y}+7 \mathrm{z} &=0 \\ 2 \mathrm{x}-\mathrm{y}+4 \mathrm{z} &=1 / 2 \\ \mathrm{x}-\mathrm{y}+\mathrm{z} &=1 \\ 6 \mathrm{x}-4 \mathrm{y}+10 \mathrm{z} &=3 \end{aligned} $$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine