Is it possible for a 5×5 matrix to be invertible when its columns do not span set of real numbers r^5? why or why not? select the correct choice below.
a. it is not possible; according to the invertible matrix theorem an n times nn×n matrix cannot be invertible when its columns do not span set of real numbers r^n.
b. it is possible; according to the invertible matrix theorem an n times nn×n matrix can be invertible when its columns do not span set of real numbers r^n.
c. it will depend on the values in the matrix. according to the invertible matrix theorem, a square matrix is only invertible if it is row equivalent to the identity.
d. it is possible; according to the invertible matrix theorem all square matrices are always invertible.

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.