How do you find u=6w+2z given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?
2 Answers
Explanation:
Find
This is essentially a substitution problem and you need to remember that when adding vectors you add corresponding components. So
# bb ul u = << 18,36,2 >> #
Explanation:
We have:
# bb ul v = << 4,-3,5 >>#
# bb ul w =<< 2,6,-1 >>#
# bb ul z =<< 3,0,4 >>#
Then, to compute
# bb ul u = 6bb ul w+2bb ul z #
# \ \ \ = 6<< 2,6,-1 >> + 2<< 3,0,4 >> #
# \ \ \ = << 6*2,6*6,6*(-1) >> + << 2*3,2*0,2*4 >> #
# \ \ \ = << 12,36,-6 >> + << 6,0,8 >> #
# \ \ \ = << 12+6,36+0,-6+8 >> #
# \ \ \ = << 18,36,2 >> #
Note that