Juan owes his cousin, Benito, $10.00. Benito is tired of waiting for Juan to pay him back. To try and get Juan to pay up more qu
ickly, Benito has decided to add $1.00 per day to the amount Juan owes him. Juan also owes his brother, Tavon, $15.00. Tavon liked Benito's idea of charging additional money, but because he is Juan's brother, decided he would only charge $.50 per day. Write and solve an equation that shows the number of days it will take for Juan to owe Benito and Tavon the same amount of money.
2 answers:
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Answer:
Linearly Dependent for not all scalars are null.
Step-by-step explanation:
Hi there!
1)When we have vectors like we call them linearly dependent if we have scalars
as scalar coefficients of those vectors, and not all are null and their sum is equal to zero.
When all scalar coefficients are equal to zero, we can call them linearly independent
2) Now let's examine the Matrix given:
So each column of this Matrix is a vector. So we can write them as:
Or
Now let's rewrite it as a system of equations:
2.1) Since we want to try whether they are linearly independent, or dependent we'll rewrite as a Linear system so that we can find their scalar coefficients, whether all or not all are null.
Using the Gaussian Elimination Method, augmenting the matrix, then proceeding the calculations, we can see that not all scalars are equal to zero. Then it is Linearly Dependent.