109 Answered Questions for the topic Linear

11/16/14

Find a set of vectors

Find a set of vectors {u,v} in R4 that spans the solution set of the equations  x-y+z-3w=0 x+2y-z+3w=0   u=? v=?

11/16/14

Determine a non trivial linear relation

Let A= [0,3,0,5] B=[2,-3,-1,-1] C=[2,21,8,33] D=[-2,6,4,4]    they are linearly dependent, determine a non-trivial linear relation 

11/15/14

For what value of h is y in the plane spanned by v1 and v2?

Let v1= [1,2,-1], v2=[-2,-1,1], and y=[4,-1,h].  For what value of h is y in the plane spanned by v1 and v2?

11/13/14

Express the vector v as a linear combination of x and y

Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1]. v=?x+?y

11/13/14

Determine a non trivial linear relation

Let A=[0,3,0,5], B=[2,-3,-1,-1], C=[2,21,8,33], and D=[-2,6,4,4]   We know that they are linearly dependent   1) Determine a non-trivial linear relation (a non trivial linear relation is three... more

11/12/14

Find two linearly independent vectors perpendicular to vector v

Find two linearly independent vectors perpendicular to the vector v=[-2,3,-5]

11/12/14

For what value of h is y in the plane?

let v1=[1,2,-1]  v2=[-2,-1,1] and y=[4,-1,h]   For what value of h is y in the plane spanned by v1 and v2? h=?

11/12/14

Find vectors u and v

Let W be the set of all vectors of the form [2s-4t,-2s,-2s+t,3s-3t] Find vectors u and v such that W=span {u,v} u=? v=?

11/12/14

Find a vector in R3

Let H be the set of all vectors of the form [-4s,-3s,5s]. Find a vector v in R3 such that H=Span{v} v=?

11/12/14

express the vector v as a linear combination

Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1] v=?x+?y

11/09/14

Find a vector v in R3 such that H=span(v)

Let H be the set of all vector of the form [-4s,-3s,5s]. Find a vector v in R3 such that H=span {v} v=?

11/02/14

Find the shortest distance from the point P

Find the shortest distance from the point P= (7, 6, 4 ) to a point on the line given by l: (x,y,z) = (-7t,7t,1t).The distance is=?

10/31/14

Find the shortest distance from Point P

Find the shortest distance from the point P= (7, 6, 4 ) to a point on the line given by l: (x,y,z) = (-7t,7t,1t). The distance is=?

10/30/14

The crossproduct of the dots are

You are looking down at a map. A vector U with |U| 1 points north and a vector V with |V|= 9 points northeast. The crossproduct UxV points:A) south?B) northwest?C) up?D) down ?   The magnitude... more

10/29/14

Among all the unit vectors find the one for which the sum is minimal

Among all the unit vectors u= <x,y,z> in R3, find the one for which the sum x + 2y + 5z is minimal.    u=<>?

10/29/14

Find a unit vector with positive first co-ordinate

Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-5, -5, -4), Q = (-1, -1, 0), and R = (-1, -1, 5).

10/29/14

Find tan theta

If vec{v} times vec{w} = <2,5,4> and vec{v}•vec{w} = 2, find tan(theta), where theta is the angle between vec{v} and vec{w}.   tan(theta)=  

10/27/14

Find an equation of the plane

Find an equation of the plane through the point (-3, -1, -2) and parallel to the plane 3x + 2y - 5z = -4. Do this problem in the standard way

10/27/14

Find the point of intersection of the two lines

Consider the two lines L1:  x = -2t, y = 1 + 2t, z = 3t and L2:  x = -9 + 5 s, y = 5 s, z = 2 + 4 sFind the point of intersection of the two lines.

10/27/14

Find the point P

Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -3.

10/27/14

Find an equation of the plane

Find an equation of the plane through the point (-5, -1, 1) and perpendicular to the vector (-1, 1, 5). Do this problem in the standard way

10/26/14

Find an equation of the plane

Find an equation of the plane through the point (-3, -1, -2) and parallel to the plane 3x + 2y - 5z = -4. Do this problem in the standard way

10/26/14

Find the area of the parallelogram determined by these four points

Let A = (4, 2, -4), B = (0, 1, -1), C = (5, 7, 0), and D = (1, 6, 3). Find the area of the parallelogram determined by these four points, the area of the triangle ABC, and the area of the triangle... more

10/20/14

Find a and b

Find a and b such that    [18,24,13] = a [1,-2,1] + b [4,4,3].   a=? b=?

10/20/14

Perform the following operations on the vectors

Perform the following operations on the vectors vec{u} =<4,-4,4>, vec{v}=<4,2,-4>, and vec{w} =<0,-2,-1>.(u)•vec(w)=(u•v)u=((w•w)u)•u=u•v+v•w=

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