The set real number set3 of all column vectors of length thr

The set real number set^3 of all column vectors of length three, with real entries, is a vector space. Is the subset B = {(x y z) element real number set^3 x^2 - y^2 + z^2 = 0} a subspace of real number set? Justify your answer.

Solution

(A1)1 = A; If we inverse twice a invertble matriz must result the same matrix. (kA)1 = k1A1 for nonzero scalar k; (AT)1 = (A1)T;   If the matrix is invertible, so is its transpose , and the inverse of its transpose is the transpose of its inverse , det(A1) = det(A)1. The inverse of det\'s matrix must be equal to det\'s inverted matrix. AB = I= BA. Where I denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.