The mechanics at Giuseppe’s Auto House specialize in changing fuel injection units and transmissions. Last week, they changed 5
fuel injection units and 10 transmissions and billed 70 hours. This week, they changed 8 fuel injection units and 8 transmissions and billed 64 hours. Let x represent the number of hours to change a fuel injection unit and y represent the number of hours to change a transmission.
What is the solution to the system that represents this scenario?
(5, 8)
(2, 6)
(4, 14)
(7, 8)
What is the solution to the system that represents this scenario?
(5, 8)
(2, 6)
(4, 14)
(7, 8)
2 answers:
Answer:
The solution is (2,6)
Step-by-step explanation:
Let
x-----> the number of hours to change a fuel injection unit
y-----> the number of hours to change a transmission
we know that
5x+10y=70 -----> equation A
8x+8y=64 -----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (2,6)
see the attached figure
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Answer: Yes, the given set of vectors is a linearly independent subset of R³.
Step-by-step explanation: We are given to show that the following set of three vectors is a linearly independent subset of R³ :
B = {(1, 1, 0), (1, 0, 1), (0, 1, 1)} .
Since the given set contains three vectors which is equal to the dimension of R³, so it is a subset of R³.
To check the linear independence, we will find the determinant formed by theses three vectors as rows.
If the value of the determinant is non zero, then the set of vectors is linearly independent. Otherwise, it is dependent.
The value of the determinant can be found as follows :
Since the determinant is not equal to 0, so the given set of vectors is a linearly independent subset of R³.
Thus, the given set is a linearly independent subset of R³.