Question

Compute the following linear combination.

(79.4, 58.1) + 3(-0.8, 6.3)

Answer 1

The resultant of the following linear combination is:

(77,77)

Explanation:

We are asked to find the linear combination of the expression:

(79.4, 58.1) + 3(-0.8, 6.3)

We multiply each of the term in the second coordinate by 3 .

i.e. this could also be given by:

(79.4, 58.1) + (3×-0.8, 3×6.3)

= (79.4, 58.1) + (-2.4, 18.9)

Now as there is a addition sign in between the two coordinates i.e. each of the first and the second coordinate will get added

i.e.

= (79.4+(-2.4),58.1+18.9)

= (79.4-2.4,58.1+18.9)

= (77,77)

i.e.

(79.4, 58.1) + 3(-0.8, 6.3)=(77,77)

Answer 2

(77, 77)

Explanation:

Carry out the indicated multiplication:

3(-0.8, 6.3) → (-2.4, 18.9)

Next, combine like terms:

(79.4, 58.1) + (-2.4, 18.9). In other words, combine the x terms 79.4 and -2.4 separately and then the y terms 58.1 and 18.9 separately:

(79.4, 58.1) + (-2.4, 18.9) → (77, 77)