1. (20 pts) For each of the following statements, please circleT (True) or F (False). You do not need to justify your answer. (a)T or F? Any eigenvector of a matrix is in the column space of thematrix. (b) T or F? The number of singular values of a matrix isalso its rank. (c) T or F? If A is an m × n with m < n, then thedimension of its column space is greater than the dimension of itsrow space. (d) T or F? A symmetric matrix is diagonalizable. (e) Tor F? The null space null(A) of a matrix A is orthogonal to thecolumn space of AT . (f) T or F? Zero can be the eigenvalue of anelementary matrix. (g) T or F? If W is a vector space spanned by 4vectors, them the dimension of W is 4.
