Let us say that you are sitting at a coffee shop and you want to impress your significant other by using your linear algebra skills. Suppose that you want to determine the strength of the café au lait you're drinking. You know your café au lait has a certain amount of coffee (x), it is brewed to achieve a certain strength (Sc), and it has a specific amount of milk (y) that could be whole, fat-free, or some other type (Sm). So to determine the strength of your drink, you need to know the quantity and the strength of both ingredients. You set your café au lait equation as follows: x coffee Sc + y milk Sm = z (coffee S'c milk S'm) where x is the quantity of coffee with a known strength Sc y the quantity of milk with a known strength Sm z is the volume of a cup of café au lait with the combined strength (S'c and S'm). This equation looks almost chemical, such as: x Hydrogen + y Oxygen = z H2O (water) 1. Describe the café au lait equation above. 2. Choose values of Sc, Sm and S'c, S'm as described below: Sc = 2, Sm = 4 and S'c = 1, S'm = 2 3. Describe how to set up the system of linear equations to solve for x and y.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Let us say that you are sitting at a coffee shop and you want to impress your significant other by using your
Suppose that you want to determine the strength of the café au lait you're drinking. You know your café au lait has a certain amount of coffee (x), it is brewed to achieve a certain strength (Sc), and it has a specific amount of milk (y) that could be whole, fat-free, or some other type (Sm). So to determine the strength of your drink, you need to know the quantity and the strength of both ingredients.
You set your café au lait equation as follows:
x coffee Sc + y milk Sm = z (coffee S'c milk S'm)
where
x is the quantity of coffee with a known strength Sc
y the quantity of milk with a known strength Sm
z is the volume of a cup of café au lait with the combined strength (S'c and S'm).
This equation looks almost chemical, such as:
x Hydrogen + y Oxygen = z H2O (water)
1. Describe the café au lait equation above.
2. Choose values of Sc, Sm and S'c, S'm as described below:
Sc = 2, Sm = 4 and S'c = 1, S'm = 2
3. Describe how to set up the system of linear equations to solve for x and y.
4. Determine the matrices involved in solving this system of equations.
5. Explain how to use Cramer's rule and find the values of x and y as a function of z.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
