If the null space of a 5 × 8 matrix a is 4-dimensional, what is the dimension of the column space of a? dim col a-(simplify your answer.)

 Dim Col A = 4.

Step-by-step explanation:

Since we have given that

Matrix A has 5 rows and 8 columns.

And Nul A = 4

It implies that the rank of A would be

Number of columns - Nul A =  8 - 4 =4

So, rank A = 4

so, it has dim Col A = 4 also.

But the four vector basis lie in R⁵.

Hence, Dim Col A = 4.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: