Homework SourseFind a vector x a b that ahs dt products x middot r 2 and
Find a vector x = [a b] that ahs dt products x middot r = 2 and x middot s = 5 with two given vectors r = [-2 3] and f = [4 -5] In the following equation [A]x = b [2 0 0 -4 1 0 3 -2 5] [x_1 x_2 x_3] = [b_1 b_2 b_3] Find the solution x for any b. From x = [A]^-1 b real off the inverse matrix [A]^-1. Determine c and d in the following linear combination of vectors. c [-3 +5] + d[2 6] = [0 -2], c = ? d = ? Find cos theta for v = [3 2] and w = [5 1] ![Find a vector x = [a b] that ahs dt products x middot r = 2 and x middot s = 5 with two given vectors r = [-2 3] and f = [4 -5] In the following equation [A]x](/WebImages/12/find-a-vector-x-a-b-that-ahs-dt-products-x-middot-r-2-and-1013328-1761523313-0.webp "Find a vector x = [a b] that ahs dt products x middot r = 2 and x middot s = 5 with two given vectors r = [-2 3] and f = [4 -5] In the following equation [A]x")
Solution
x.r = 2
=>
-2a+3b = 2
x.b = 5
=>
4a-5b = 5
=> a = 12.5, b=9
=> x = [12.5 9]T
3)
-3c +2d =0
5c + 6d = -2
=> c =-1/7 , d = -3/14
4)
|v| = sqrt(3^2+2^2) = sqrt(13)
|w| = sqrt(5^2 + 1) = sqrt(26)
cos a = v.w/|v| |w|
= 15+2/sqrt(13*26)
= 17/13sqrt(2)
