Consider a system of linear equations for price P and production Q as follows: 5P+Q=68, and -3P+Q=-10. Its coefficient matrix is given by \left[\begin{array}{ccc} 5&1&68 \\ -3&1&-10\end{array}\right] . Now, use forward elimination method to obtain its upper triangular form \left[\begin{array}{ccc} 1&a&13.6 \\ 0&1&19.25\end{array}\right] where a is some value you need to work out. So, what is the value of a rounded to 2 decimal places? Question 5 Answer a. 0.20 b. 0.00 c. 19.25 d. none of the others e. 0.36
Question
Consider a system of linear equations for price P and production Q as follows:
5P+Q=68, and
-3P+Q=-10.
Its coefficient matrix is given by
\left[\begin{array}{ccc} 5&1&68 \ -3&1&-10\end{array}\right] .
Now, use forward elimination method to obtain its upper triangular form
\left[\begin{array}{ccc} 1&a&13.6 \ 0&1&19.25\end{array}\right]
where a is some value you need to work out.
So, what is the value of a rounded to 2 decimal places?
Question 5 Answer
a. 0.20
b. 0.00
c. 19.25
d. none of the others
e. 0.36
Solution
To find the value of 'a', we need to perform the forward elimination method on the given system of equations.
The first step is to make the first element of the first row of the matrix a '1'. We can do this by dividing the first row by 5. This gives us:
\left[\begin{array}{ccc} 1&0.2&13.6 \ -3&1&-10\end{array}\right] .
Next, we want to make the first element of the second row a '0'. We can do this by adding 3 times the first row to the second row. This gives us:
\left[\begin{array}{ccc} 1&0.2&13.6 \ 0&1.6&30.8\end{array}\right] .
Finally, to make the second element of the second row a '1', we divide the second row by 1.6. This gives us:
\left[\begin{array}{ccc} 1&0.2&13.6 \ 0&1&19.25\end{array}\right] .
So, the value of 'a' is 0.2, which is option (a).
Similar Questions
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