If the coefficient matrix has a pivot in each column, it means that it is shaped like this:
![A=\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Da_%7B1%2C1%7D%26a_%7B1%2C2%7D%26a_%7B1%2C3%7D%26a_%7B1%2C4%7D%5C%5C0%26a_%7B2%2C2%7D%26a_%7B2%2C3%7D%26a_%7B2%2C4%7D%5C%5C0%260%26a_%7B3%2C3%7D%26a_%7B3%2C4%7D%5C%5C0%260%260%26a_%7B4%2C4%7D%5Cend%7Barray%7D%5Cright%5D)
So, the correspondant system

will look like this:
![\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]\cdot \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{c}b_1\\b_2\\b_3\\b_4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7Da_%7B1%2C1%7D%26a_%7B1%2C2%7D%26a_%7B1%2C3%7D%26a_%7B1%2C4%7D%5C%5C0%26a_%7B2%2C2%7D%26a_%7B2%2C3%7D%26a_%7B2%2C4%7D%5C%5C0%260%26a_%7B3%2C3%7D%26a_%7B3%2C4%7D%5C%5C0%260%260%26a_%7B4%2C4%7D%5Cend%7Barray%7D%5Cright%5D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx_1%5C%5Cx_2%5C%5Cx_3%5C%5Cx_4%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Db_1%5C%5Cb_2%5C%5Cb_3%5C%5Cb_4%5Cend%7Barray%7D%5Cright%5D)
This turn into the following system of equations:

The last equation is solvable for
: we easily have

Once the value for
is known, we can solve the third equation for
:

(recall that
is now known)
The pattern should be clear: you can use the last equation to solve for
. Once it is known, the third equation involves the only variable
. Once
Answer: -7
Step-by-step explanation:
The equation is in slope-intercept form (y=mx+b), where m is the slope and b is the y-intercept
Therefore, the m value is -7 and it is the slope
Answer:
<u>(x² + 4x + 6)/ 3x + 12</u>
<u>This is the most simplified form</u>
Step-by-step explanation:
Let's simplify the expression:
(x + 6)/(x + 4) + (x - 3)/3
Least Common Denominator : 3 * (x + 4)
[3 * (x + 6) + (x - 3) (x + 4)]/ 3 * (x + 4)
Solving parentheses:
[3x + 18 + x² - 3x + 4x - 12]/ 3 * (x + 4)
Like terms:
<u>(x² + 4x + 6)/ 3x + 12</u>
<u>This is the most simplified form</u>
Answer:
The estimated distance is 405 meter.
Step-by-step explanation:
Given : Your velocity is given by
in m/sec, with t in seconds.
To find : Estimate the distance, s, traveled between t=0 and t=8 ?
Solution :
We have to integrate the function from 0 to 8 to get the distance.
Integrate
w.r.t t,

We know, 
![=[\frac{2t^3}{3}+8t]^8_0](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B2t%5E3%7D%7B3%7D%2B8t%5D%5E8_0)





The estimated distance is 405 meter.