All vectors and subspaces are in RnR n. Mark each statement True or False. Justify each answer. a. Not every linearly independent set in RnR n is an orthogonal set.
b. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be computed without row operations on a matrix.
c. If the vectors in an orthogonal set of nonzero vectors are normalized, then some of the new vectors may not be orthogonal.
d. A matrix with orthonormal columns is an orthogonal matrix.
e. If L is a line through 0 and if ˆyy^ is the orthogonal projection of y onto L, then ∥ˆy∥∥ y^ ∥ gives the distance from y to L.

What point is the projection of q on a) r b) s c) t

Which of the following is the sum of 3 1/6 + 6 3/8?

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)