(Answered)-The cartesian equation of a 2-dimensional plane in R4 is Nx = d - (2025 Updated Original AI-Free Solution

Question

1. The cartesian equation of a 2-dimensional plane in R4 is Nx = d where N is a 2 ? 4 matrix with rankN = 2, x is a column vector in R4, and d is a column vector in R2.?
   1. (a) ?Show that the intersection of two 2-dimensional planes in R4 can be reduced to a system of linear equations of the form Ax = b where A is a 4?4 matrix, x and b are column vectors in R4. Carefully show that rankA is at least 2.?
   2. (b) ?Classify the possible ways that two 2-dimensional planes in R4 can intersect using the rank of A and M.?
   3. (c) ?Give a simple example of two 2-dimensional planes in R4 that intersect in a line containingthepointx1 =1,x2 =2,x3 =3,x4 =4.