Question: Problem 1(6 points) Are the following statements true or false? T F Suppose A is a 3 x 3 matrix with columns v1, v2, 03:

Problem 1(6 points) Are the following statements true or false? T F Suppose A is a 3 x 3 matrix with columns v1, v2, 03: A = [v1 |v2|v3]. If v2 = 347v3 + 621v1, then A is invertible. T F For a matrix A we always have: row(A) = null(A). T F If dim(W) = 3 and dim(WI) - 2, then W is a subspace of R6. T F Similar matrices have the same eigenvalues. T F If the characteristic polynomial of a 5 x 5 matrix A is det(A - XI) = 13(X - 3)() - 1), then A has rank 5. T F If A is a 4 x 4 matrix so that the algebraic multiplicities of all eigen- values are equal to 1, then A has to be diagonalizable

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