Homework Statement
find the dimension of the linear span of the given vectors
v1 = ( 2, -3, 1) v2 = ( 5, -8, 3) v3 = (-5, 9, -4)
Homework Equations
The Attempt at a Solution
so all i did was make it a matrix and put it in rref and i got
[1 0 0]
[0 1 0]
[0 0 1]
does this...
Homework Statement
P is the point where the diagonals of the parallelogram abcd intersect one another
let \alpha = AB and \beta = AD and let s and t be scalars such that AP = sAC and BP = tBD
use vector algebra to show that
s(\alpha + \beta) = AP = \alpha + t(\beta - \alpha)The Attempt at...
OH K, so that's what i initially did then
i had x = -3 +t(3-1) => x = -3 +2t
y = 4 + t(1-4) => y = 4 -3t
then i got
t= (x+3)/2 and t = (y - 4)/ -3
making both equations equal each other i get
-3x -9 = 2y -8
-3x -2y -1 = 0
3x +2y + 1 = 0
sorry i mean x = -3 +t(-1,3)
y = 4 + t(1, -4)
which gives me x = -3 + 2t and y = 4 + -3t
i then isolate for t, make the equations equal to each other and i get 3x + 2y + 1 = 0
Homework Statement
assume the existence of a fixed coordinatization of the plane in which 0 is the origin. Find an equation and give the coordinates of a third point that is on the line a:(-3,4) b:(1,1)
Homework Equations
The Attempt at a Solution
ok so i get x = -3 + t(-1 3)
y...