Can you please check these answers.
In exercises 10-13 , find (a)2v+u, (b)u-3v), and (c)5u-v.
10.u=<0,-4>, v=<-2,-8>
a) 2v+u
= <-4,-16) + <0,-4)
= <-4, -20>
b,u-3v
=<0,-4>- <-6,-24>
=<6,20>
c) 5u - v
= <0,-20> - <-2,-8)
= <2, -12>
11.u=<-2,-3>, v=<-1,-10>
a,2v+u
=<-2,-20>+<-2,-3>
=<-4,-23>
b,u-3v
=<-2,-3>-<-3,-30>
=<1,0>
c,5u-v
=<-10,-15>-<-1,-10>
=<-9,-5>
u=i-j v=6i+9i
a. 2v+u
u=i-j, v=6i+9i
=(12i+18j) + (i-j)
=13i+ 17j
b. u-3v
(i-j)-(18i+27i)
-17i - -26j
c. 5u-v
(5i-5j)-(30i+54j)
-25i - -59j
u=2i+3j, v= -i-2j
U=2i+3j, v=-i-2j
a. 2v+u
-2i+-4j + 2i+3j
0, -j
b. U-3v
2i+3j –(-3i)-6j
5i-(-3j)
c. 5u-v
10i+15j – (-i)-2j
11i-13j
I checked the first 4, they were ok
you seem to know what you are doing.
Let's go through each example and verify the answers.
Example 10:
u = <0, -4>, v = <-2, -8>
a) To calculate 2v + u, we perform scalar multiplication on v by 2 and then add u.
2v = 2 * <-2, -8> = <-4, -16>
2v + u = <-4, -16> + <0, -4> = <-4, -20>
The answer is correct: 2v + u = <-4, -20>
b) To calculate u - 3v, we perform scalar multiplication on v by -3 and then subtract it from u.
-3v = -3 * <-2, -8> = <-6, -24>
u - 3v = <0, -4> - <-6, -24> = <6, 20>
The answer is correct: u - 3v = <6, 20>
c) To calculate 5u - v, we perform scalar multiplication on u by 5 and then subtract v.
5u = 5 * <0, -4> = <0, -20>
5u - v = <0, -20> - <-2, -8> = <2, -12>
The answer is correct: 5u - v = <2, -12>
Example 11:
u = <-2, -3>, v = <-1, -10>
a) To calculate 2v + u, we perform scalar multiplication on v by 2 and then add u.
2v = 2 * <-1, -10> = <-2, -20>
2v + u = <-2, -20> + <-2, -3> = <-4, -23>
The answer is correct: 2v + u = <-4, -23>
b) To calculate u - 3v, we perform scalar multiplication on v by -3 and then subtract it from u.
-3v = -3 * <-1, -10> = <-3, 30>
u - 3v = <-2, -3> - <-3, 30> = <1, -33>
The answer has an error: u - 3v = <1, -33>, not <1, 0>.
c) To calculate 5u - v, we perform scalar multiplication on u by 5 and then subtract v.
5u = 5 * <-2, -3> = <-10, -15>
5u - v = <-10, -15> - <-1, -10> = <-9, -5>
The answer is correct: 5u - v = <-9, -5>
Example 12:
u = <2, 3>, v = <-1, -2>
a) To calculate 2v + u, we perform scalar multiplication on v by 2 and then add u.
2v = 2 * <-1, -2> = <-2, -4>
2v + u = <-2, -4> + <2, 3> = <0, -1>
The answer is correct: 2v + u = <0, -1>
b) To calculate u - 3v, we perform scalar multiplication on v by -3 and then subtract it from u.
-3v = -3 * <-1, -2> = <3, 6>
u - 3v = <2, 3> - <3, 6> = <-1, -3>
The answer is correct: u - 3v = <-1, -3>
c) To calculate 5u - v, we perform scalar multiplication on u by 5 and then subtract v.
5u = 5 * <2, 3> = <10, 15>
5u - v = <10, 15> - <-1, -2> = <11, 17>
The answer has an error: 5u - v = <11, 17>, not <11, -13>.
It seems that there was a mistake in Example 11 (b) and Example 12 (c). Please make sure to double-check the calculations in those steps.