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3 years ago

How many factors of 2 are there in 2³? answers> 1 2 3 5

Mathematics

1 answer:

algol [13]3 years ago

6 0

Answer:

Step-by-step explanation:

2^3= 2*2*2

factors of 8= 1,2,4,8

factors of 2= 1,2

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For problem (1) and (2), use Gauss-Jordan reduction to transform the augmented matrix of each system to RREF. Use it to discuss

kogti [31]

Answer:

The system has unique solution.

$\therefore x=-\frac57$ , $y=\frac57$ and $z=-\frac{30}{7}$

Step-by-step explanation:

Given system of equation is

2x+3y+z=5

2x+9y+0.z=5

12x+y+3z=5

The augmented matrix is

$\left[\begin{array}{ccc}2&3&1\\2&9&0\\12&1&3\end{array}\right|\left\begin{array}{c}5\\5\\5\end{array}\right]$

Subtract row 1 from row 2 ( $R_2=R_2-R_1$ )

$\left[\begin{array}{ccc}2&3&1\\0&6&-1\\12&1&3\end{array}\right|\left\begin{array}{c}5\\0\\5\end{array}\right]$

subtract row 1 multiplied by 6 from row 3 ( $R_3=R_3-6R_1$ )

$\left[\begin{array}{ccc}2&3&1\\0&6&-1\\0&-17&-3\end{array}\right|\left\begin{array}{c}5\\0\\-25\end{array}\right]$

Divide row 1 by 2 ( $R_1=\frac{R_1}2$ )

$\left[\begin{array}{ccc}1&\frac32&\frac12\\0&6&-1\\0&-17&-3\end{array}\right|\left\begin{array}{c}\frac52\\0\\-25\end{array}\right]$

Divide row 2 by 6 $(R_2=\frac{R_2}6)$

$\left[\begin{array}{ccc}1&\frac32&\frac12\\ \\0&1&\frac{-1}{6}\\ \\0&-17&-3\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\-25\end{array}\right]$

Subtract row 2 multiplied by $\frac32$ from row 1 $(R_1=R_1-\frac32 R_2)$

$\left[\begin{array}{ccc}1&0&\frac34\\ \\0&1&\frac{-1}{6}\\ \\0&-17&-3\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\-25\end{array}\right]$

Add row 2 multiplied by 17 to row 3 $(R_3=R_3+17R_2)$

$\left[\begin{array}{ccc}1&0&\frac34\\ \\0&1&-\frac{1}{6}\\ \\0&0&-\frac{35}{6}\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\-25\end{array}\right]$

Multiply row 3 by $-\frac{6}{35}$ $(R_3=-\frac6{35} R_3)$

$\left[\begin{array}{ccc}1&0&\frac34\\ \\0&1&-\frac{1}{6}\\ \\0&0&1\end{array}\right|\left\begin{array}{c}\frac52\\ \\0\\ \\\frac{30}7\end{array}\right]$