Please I need help in solving this questions

1. Let A = ( 2 3 1

3 8 2 ) and define G(x) = Ax. Find all vectors x ³

so that G(x) = ( 2

3 ).

2. Let A be the matrix in the previous exercise, and b = ( 2

1

2 ).

Is b in the range of the linear transformation x Ax? Why or why not?

3. Let A = ( 1 2 3

4 5 6

7 8 9 ) and B= (a 0 0

0 a 0

0 0 a ) where a is a real number.

a. AB =

b. BA =

c. Describe the effect on the columns or rows of A when AD or DA is created.

4. Let A = ( 1 2 3

4 5 6

7 8 9 ).

a. Give a matrix E so that EA is the matrix obtained from A from the ERO 2R₁ + R₂ R₂.

b. Give a matrix E so that EA is the matrix obtained from A from the ERO R₂ R₃.

c. Give a matrix E so that EA is the matrix obtained from A from the ERO 3R₂ R₂.