Por favor contesten en a y b

mylen [45]

i thinks its b......................

5 0

3 years ago

In Exercises 40-43, for what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infini

svet-max [94.6K]

Answer:

If k = −1 then the system has no solutions.

If k = 2 then the system has infinitely many solutions.

The system cannot have unique solution.

Step-by-step explanation:

We have the following system of equations

$x - 2y +3z = 2\\x + y + z = k\\2x - y + 4z = k^2$

The augmented matrix is

$\left[\begin{array}{cccc}1&-2&3&2\\1&1&1&k\\2&-1&4&k^2\end{array}\right]$

The reduction of this matrix to row-echelon form is outlined below.

$R_2\rightarrow R_2-R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\2&-1&4&k^2\end{array}\right]$

$R_3\rightarrow R_3-2R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&3&-2&k^2-4\end{array}\right]$

$R_3\rightarrow R_3-R_2$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&0&0&k^2-k-2\end{array}\right]$

The last row determines, if there are solutions or not. To be consistent, we must have k such that

$k^2-k-2=0$

$\left(k+1\right)\left(k-2\right)=0\\k=-1,\:k=2$

Case k = −1:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-1-2\\0&0&0&(-1)^2-(-1)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-3\\0&0&0&-2\end{array}\right]$

If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.

Case k = 2:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&2-2\\0&0&0&(2)^2-(2)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&0\\0&0&0&0\end{array}\right]$

This gives the infinite many solution.

5 0

3 years ago

The distance between Taylor’s house and her school is 300,000 centimeters.

Sergio [31]

Answer:

30 km

Step-by-step explanation:

1 kilometer = 100 meters.

1 meter = 100 cm

therefore, 1 km = 10,000

and then, 300000 cm is 30 km

7 0

4 years ago

Solve for x: 3-(2x-5)<-4(x+2)

trapecia [35]

3-(2x-5)=-4(x+2)

We simplify the equation to the form, which is simple to understand
3-(2x-5)=-4(x+2)

Remove unnecessary parentheses
3-2x+5=-4*(x+2)

Reorder the terms in parentheses
3-2x+5=+(-4x-8)

Remove unnecessary parentheses
+3-2x+5=-4x-8

We move all terms containing x to the left and all other terms to the right.
-2x+4x=-8-3-5

We simplify left and right side of the equation.
+2x=-16

We divide both sides of the equation by 2 to get x.
x=-8

6 0

3 years ago

Read 2 more answers

Mandy drives to work every day. The distance she travels is given by the equation d = 4.5t, where d is the distance traveled and

Anastasy [175]

The constant is "4.5 miles per hour", or whatever the actual units are.

3 0

3 years ago

Read 2 more answers

Por favor contesten en a y b​

Por favor contesten en a y b