Write the augmented matrix for each system of equations. 9x-4y-5z=9 7x+4y-4z=-1
2 answers:
Answer:
The augmented matrix is:
Step-by-step explanation:
<u>Augmented matrix:</u>
It is a matrix form of a linear system of equations obtained from the coefficient matrix. It is created by adding an additional column of for the constants on the right hand side of the equal sign.
Here we are given a system of linear equations as:
and
Hence, the augmented matrix formed is as follows:
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To solve this we are going to use the future value of annuity due formula: ![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bkt%7D-1%20%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where
is the future value
is the periodic deposit
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the number of deposits per year
We know for our problem that
and 
. To convert the interest rate to decimal form, we are going to divide the rate by 100%: 
. Since Ruben makes the deposits every 6 months, 
. The interest is compounded semiannually, so 2 times per year; therefore, .
Lets replace the values in our formula:
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We can conclude that the correct answer is <span>$29,299.53</span>
where
We know for our problem that
Lets replace the values in our formula:
We can conclude that the correct answer is <span>$29,299.53</span>