If the nullity of an 8 times 5 matrix A is 2 what is the dim

If the nullity of an 8 times 5 matrix A is 2 what is the dimension of Row(A)? If A is a 4 times 3 matrix, what is the largest possible dimension of the row space of A? Explain If A is a 3 times 4 matrix what is the largest possible dimension of the row space of A? Explain If A is a 6 times 8 matrix, what is the smallest possible value for the nullity of A? If A is a 6 times 4 matrix, what is the smallest possible value for the nullity of A? Mark each answer true or false and justify your answer: The row space of A is the same as the column space of A^T If B is the row-echelon form of A, and if B has three nonzero rows, then the first three rows of A form a basis for Row(A) Dim Row(A) + nullity(A) = number of rows in A. Suppose A is an m times n matrix. Which of the subspaces Row(A), col(A), Null(A), Row(A^T), col(A^T), and Null(A^T) are in R^m and which are in R^n? How many distinct subspaces are in this list?

Solution

7) 8x5 matrix has 5 columns

nullity is 2 dim it means it has 5 coulumns with 3 pivots

hence there will be 3 non zero rows in the matrix

so, dim of row is 3

8)    in 4x3 matrix

there are 3 columns , hence atmost 3 pivots

therefore, larghest possible dimension of row space would be 3