Determine
whether b can be written as a linear
combination of a1 and a2. in other words, determine
whether weights x1 and x2 exist, such that x1a1 + x2a2 = b. determine the
weights x1 and x2 if possible.
a1[4,5,-4]
a2[-4,3,3] b,[8,26,-10]

Step-by-step explanation:

Linear Combination Of Vectors

One vector is a linear combination of and if there are two scalars such as

In our case, all the vectors are given in but there are only two possible components for the linear combination. This indicates that only two conditions can be used to determine both scalars, and the other condition must be satisfied once the scalars are found.

We have

We set the equation

Multiplying both scalars by the vectors

Equating each coordinate, we get

Adding the first and the third equations:

Replacing in the first equation

We must test if those values make the second equation become an identity

The second equation complies with the values of and , so the solution is

y = -1

x = 8

hope this !