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.

the answer is 15% decrease

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.