The area of a parallelogram in R², built on non-parallel vectors v₁,v₂and the volume of a parallelepiped in R³, built on vectors v₁, v₂, v₃, which do not lie in the same plane, is |det A|(or abs(det A)), where A=[v₁v₂] and A=[ v₁v₂v₃], respectively.

To be given is 2 vectors in R², v₁and v₂, or 3 vectors in R³, v₁, v₂, and v₃, on which a parallelogram or parallelepiped, respectively, may or may not be built.

**How would you create a function in MATLAB for:

function D = areavol(A)

which takes as an input a matrix A, whose columns are the vectors on which a parallelogram or parallelepiped may possibly be built.

**First, your function has to check whether the given vectors are linearly independent. I recommend using the functionrankto verify that. If it is not the case, then a parallelogram in R²or parallelepiped in R³cannot be built. In this case, the function (1) outputs a message, which has to be specific about whether a parallelogram or a parallelepiped cannot be built,

(2) it also outputs D=0, and the program terminates (the commandreturn).

**If the vectors are linearly independent, the function calculates the area or the volume, denoted D, and outputs one of the following messages with the value of D:

"The area of the parallelogram is" (output the area D)

or

"The volume of the parallelepiped is" (output the volume D)

Hint: in order to display a correct message whether it is the area or the volume, you should keep a track on the number of columns of A and use a conditional statement.