110 SolutionLet A 1 4 7 5 1 0 1 4 3 1 2 6 6 4 0 We will red

Solution

Let A =

1

-4

7

-5

-1

0

1

-4

3

1

2

-6

6

-4

0

We will reduce A to its RREF as under:

Add -2 times the 1st row to the 3rd row

Add -2 times the 2nd row to the 3rd row

Add 4 times the 2nd row to the 1st row

Then the RREF of A is

1

0

-9

7

3

0

1

-4

3

1

0

0

0

0

0

Apparently, b = (-1,1,0)^T = 3(1,0,2)^T +1(-4,1,-6)^T . Thus, b is in Range of the linear transformation x Ax.