Let 7': R" + R be a linear transformation whose matrix representation is 0 ] = 2 3 Gauss-Jordan reduction applied to [?'] yields the matrix B = OOHO DON and ap- 1 0 1 3 0 1 1 plied to the transpose of [?'] yields C = 0 0 0 0 0 0 0 0 (a) From the matrices above we can read off the dimension of the range of T' and write down a basis for it. Explain carefully. (b) From the matrices above we can read off the dimension of the range of the transpose of T' and write down a basis for it. Explain carefully. (c) From the matrices above we can write down two equations which a vector (v, w, I, y, =) must satisfy to be in the kernel of 7. Explain carefully. What are the equations? Also explain carefully how we obtain from these equations the dimension of the kernel of T' and find a basis for it. Carry out the calculation you describe. (d) From the matrices above we can write down two equations which a vector (w, I, y, =) must satisfy to be in the kernel of the transpose of 7'. Explain carefully. What are the equations? Also explain carefully how we obtain from these equations the dimension of the kernel of 7" and find a basis for it. Carry out the calculation you describe