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The cartesian equation of a 2-dimensional plane in R4is Nx = d where N is a 2 4matrix with rank N = 2, x is a column vector in R4, and d is a column...

The cartesian equation of a 2-dimensional plane in R4is Nx = d where N is a 2 × 4matrix with rank N = 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 R4can be reduced to asystem of linear equations of the form Ax = b where A is a 4 × 4 matrix, x and bare column vectors in R4. Carefully show that rank A is at least 2.

(b) Classify the possible ways that two 2-dimensional planes in R4can intersect usingthe rank of A and M.

(c) Give a simple example of two 2-dimensional planes in R4that intersect in a linecontaining the point x1 = 1, x2 = 2, x3 = 3, x4 = 4.

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