Question: Please provide a step by step method as I have not worked with an example where the RS is given rather than the matrix it

Please provide a step by step method as I have not worked with an example where the RS is given rather than the matrix it self. Thank You

Please provide a step by step method as I have
Let M be a 4 x 4 symmetric matrix whose row space, RS(M), is the subspace of R given by RS(M) = 2 2 E R4 X1 - X2 = 0, X2 - 23 = 0 and 231-24 -0. (i) Express N(M), the null space of M, as the linear span of a suitable set of vectors in R4. (ii) Express CS(M), the column space of M, as the linear span of a suitable set of vectors in R 4 . (iii) Find the most general matrix M whose null space and column space are those found in parts (i) and (ii). (iv) Given the additional information that 1 = 8 is one of the eigenvalues of M, find all the eigenvalues of M and state the geometric multiplicity of each eigenvalue, explaining your answer. (v) Hence find the numerical entries of M

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