Question: a) If a matrix has an eigenvalue with 2=0, what can you decide about the rank and columnspace of the matrix? Is it a matrix

a) If a matrix has an eigenvalue with 2=0, what can you decide about the rank and columnspace of the matrix? Is it a matrix with full rank as column? Do the columns span the whole vectorspace? b) Are all the eigenvectors of a real symmetric matrix can be chosen perpendicular to each other? How do you prove it? c) Find the Singular Value Decomposition (SVD) of the following matrix and mention at least two applications of SVD. A = 2 2 3 -2

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