B needed with all sub partsKindly solve ASAPPlease do now In will like your work if you did it for me A. All about that Basis IIFind the matrix P that transforms S₁ to S₂ for the following pairs of bases.1. S₁ = {(2,5), (1, 1)}, S₂ = {(1, 3), (0, 2)}2. S₁ = {(1,0), (0, 1)}, S₂ = {(a, b), (c,d)}3. S₁ = {(a, b), (c,d)}, S₂ = {(1,0), (0, 1)}4. What conditions on a,b, c, and d make part (c) impossible? Why?B. Fun SubspacesConsider the following 3 x 4 matrix A and its Reduced Row Echelon form, denoted U.[1 2 0 1][1 0-4 17A 0 1 20 U= 01 2 01 20100 0 07.1. Find a basis and dimension for the four fundamental subspaces of A and U.2. Which of the four fundamental spaces of A have the same dimension as those of U?If so, why?3. Which of the four fundamental spaces of A are equal to those of U? If so, why?Note that parts (1) and (3) are asking different questions. Not all subspaces of equaldimension are equivalent.

It is given that A=120101201201 and U=10-4101200000 is its Reduced Row Echelon form. 1. The…

B. Fun Subspaces Consider the following 3 x 4 matrix A and its Reduced Row Echelon form, denoted U. [1 2 0 1 A = 0 1 20 1 2 0 1 - [10 -4 1 U = 0 1 2 [0000] 0 1. Find a basis and dimension for the four fundamental subspaces of A and U. 2. Which of the four fundamental spaces of A have the same dimension as those of U? If so, why? 3. Which of the four fundamental spaces of A are equal to those of U? If so, why? Note that parts (1) and (3) are asking different questions. Not all subspaces of equal dimension are equivalent.