Lets say A can be reduced to the following matrix using row operations: 1 80 0 0 0 10 -10 0 0 0 1 0 0 0 0 4 8 a) Determine the pivot columns, the basic variables and the free variables. Write the solution to Ax = 0 in parametric vector form. b) Does Ax = b have a solution for every possible b?

Let the Matrix A =( 1 -2 -6 , 0 3 7 , 1 -2 5 ) and vector b = (11 , -5 , 9 ) is b in the span of the column space A ?

must solve all parts for upvote

Let -1 -8 A = 1 0 0 1 Is A diagonalizable? If yes, find the matrix P that diagonalize A. Further, find A100.

Describe and compare the solution sets of x₁ +5x₂ - 2x3 = 0 and x₁ + 5x₂ - 2x3 = -7. X1 E Describe the solution set, x= x₂ of x₁ +5x₂ - 2x3 = 0 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. X3 (Type an integer or fraction for each matrix element.) OA. X= O B. X=X3 C. X=X₂ O D. X= + X3 X1 E x2 of x₁ + 5x₂ - 2x3 = = -7 in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice. x3 (Type an integer or fraction for each matrix element.) OA. X= B. X= +X₂ Describe the solution set, x = O c. x= O D. X=X₂ +X3 +x₂ + X3 +X3 Which option best compares the two equations? O A. The solution set of the second equation is a plane perpendicular to the line that is the solution set of the first equation. O B. The solution set of the second equation is a plane parallel to the plane that is the solution set of the first equation. OC. The solution set of the second equation is a plane parallel to…

Please solve all four parts, else skip it.

Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. [:::) 1 2 0 - 3 3 6 0 - 9 x=x+x+xO X= X2 + X3 +X4 (Type an integer or fraction for each matrix element.)