Question

a) If A is a 3 x 6 matrix and Rank(A) = 2, then what is the dimension of Nul(A)? b) If B is a 8 x 5 matrix and the dimension of Nul(B) = 3, what is the dimension of Col(B)? c) If C is a 4 x 8 matrix, what is the largest possible dimension of Row(C)?

Answer 1

I u A is a 3x6 Matrin 2183 T and As Rank A= 2. dim Rank A tám Nullity A = din A at dim NAD = diamNial = I'm Nulchis u dima 6-2 dim NCAI=4 IL B is 8x8 Matrix . Bi IRS R8 - dim RowB= dimals - f dim Nul(BI= 3. = Rook I'm Col (BI= ? .. dimm Caliol = 2 r Rank B = 5-dimo WB . RankB = 5-3=2 dim Calisia s No. of Columns of marrin = {: 3+275).

% If c is 4x8 matsin ie C IRBTIR dunension of Rowro - As - it is Possible Onto so Rank (c) = . (c)- į Largest possible Dimensions of Row CCI= 4 CHINATHATATLANTANYA