Assignment

1) Use appropriate algorithmic way to justify if A is invertible. Find A^-1 if that exists by using the algorithm.

Now answer the followings with explanation:

(i) Is A^T invertible? If so write it's inverse without any elementary row operation.

(ii) Let B and C be any two invertible 4x4 matrix. How many solutions does the equation (ABC)^TX = 0 have?

2) Does the columns of the following matrix span R⁶? [ DO NOT USE ROW OPERATION]

(Hint: Use some definition and some theorem)

3) Let A be the Matrix of the Linear Transformation T: R⁶ → R⁶ given by

T ((x₁, x₂, x₃, x₄, x₅, x₆) = (2x₁ - x₂, 3x₁, 2x₃ - x₄, 3x₃, 2x₅ - x₆, 3x₆)

Is T invertible? If so find a formula for T^-1 as in the form of T. [DO NOT USE ROW OPERATION]