(Solved by Humans)-The cartesian equation of a 2-dimensional plane in R4 is Nx = d
Question
- 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.??
- (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.?
- (b) ?Classify the possible ways that two 2-dimensional planes in R4 can intersect using the rank of A and M.?
- (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.
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