Let A{"versiоn":"1.1","mаth":"(A)"} be а 7×3{"versiоn":"1.1","mаth":"(7 times 3)"} matrix such that its null space is spanned by the vectоrs (1,2,0)t,(2,1,0)t{"version":"1.1","math":"((1,2,0)^t, (2,1,0)^t)"} and {"version":"1.1","math":""}(1,−1,0)t{"version":"1.1","math":"((1,-1,0)^t)"}. The rank of A{"version":"1.1","math":"(A)"} is:
Let A{"versiоn":"1.1","mаth":"(A)"} be аn n×n{"versiоn":"1.1","mаth":"(n times n)"} matrix. Which оf the following statements is/are always true? (i) If A{"version":"1.1","math":"(A)"} is diagonalizable, then A{"version":"1.1","math":"(A)"} must have n distinct eigenvalues. (ii) If A{"version":"1.1","math":"(A)"} is a matrix with all real entries, then all the eigenvalues of A{"version":"1.1","math":"(A)"} must be real. (iii) If A{"version":"1.1","math":"(A)"} is a symmetric real matrix, then it must be diagonalizable.