LINEAR ALGEBRA Suppose u1= [2,3,1] and u2= [4,1,0]. For which value(s) of the constant k is [1,2,k] a linear combination of u1 and u2?

The value of the constant so that is a linear combination of and is .

Step-by-step explanation:

Let be , and , is a linear combination of and if and only if:

(Eq. 1)

Where:

, , - Scalar coefficients of linear combination, dimensionless.

By dividing each term by :

(Eq. 2)

- Zero vector, dimensionless.

And all vectors are linearly independent, meaning that at least one coefficient must be different from zero. Now we expand (Eq. 2) by direct substitution and simplify the resulting expression:

The following system of linear equations is obtained:

(Eq. 3)

(Eq. 4)

(Eq. 5)

The solution of this system is:

, ,

The value of the constant so that is a linear combination of and is .

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

47

step-by-step explanation: