use the power method to approximate the dominant eigenvalue and eigenvector of A. Use the given initial vector x0 , the specified number of iterations k, and three-decimal-place accuracy. A c14 125 3 d , x0 c11d , k 5

Math241Lecture 2: Equation of planes, Quadratic Surfaces Recall from the previous lecture that we can find an equation of a line just by knowing a point on the line and a vector parallel to the line. We can do a similar thing with the equation of a plane. Say we know a point P on the plane with coordinates P=(x ,y,z) . Next, say we want a vector perpendicular to the point. We call that a normal vector and denote it as ⃗=¿a,b,c>¿ . We do not need that the normal vector is on the plane. It just has to be P perpendicular to it. Now let’s take a random point on the plane and call it with coordinates P1=(x 1 y 1z 1 r r1 P . We let the position vectors and be the position vectors for and P 1 respectively. So the normal vector and the difference of the two position vectors will be perpendicular to one another since the position vectors are on the plane. That means their dot product will be zero. n⋅(r1−r⃗)0 So the general formula for finding the equation of a plane is a(x1−x +) ( −1 +c ) (z 10 ) Now that we have a formula, let’s work an example shall we P=(1,3,2) Ex 1: Determine the equation of the plane that contains the points , Q=(−3,−1,4) and R=(1,0,3) We can form two vectors from the three points, vectors PQ and PR. ⃗ PQ=¿−4,−4,2>¿ PR=¿0,−3,1>¿ We know that t