Question

Consider the following three vectors:
A = (2,−1,1), B = (3,0,5), and C = (1,4,−2).
Calculate the following combinations. Express your answers as ordered triplets [e.g., (9,4,−2)].
a. A+Bb. B+Cc. A+B+Cd. 3A+2Ce. 2A+ 3B+Cd. 2A+3(B+C)

Answer 1

To make the sum of the vectors, we must make the sum of each of its components. Note that each comma indicates a different component and that component must be the same as that added to the other vector. If there is a number multiplying the vector, we will first proceed to perform the internal multiplication and then the sum.

A)

$A+B = (2,-1,1)+(3,0,5)$

$A+B = (5,-1,6)$

B)

$B+C = (3,0,5)+(1,4,-2)$

$B+C = (4,4,3)$

C)

$A+B+C =(2,-1,1)+(3,0,5)+(1,4,-2)$

$A+B+C = (6,3,4)$

D)

$3A+2C = 3(2,-1,1)+2(1,4,-2)$

$3A+2C = (8,5,-1)$

E)

$2A+3B+C = 2(2,-1,1)+3(3,0,5)+)+(1,4,-2)$

$2A+3B+C = (14,2,15)$

F)

$2A+3(B+C) = 2(2,-1,1)+3((3,0,5)+(1,4-2))$

$2A+3(B+C) = (16,10,11)$