4) Let V = M2x2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → (a) (b) (c) T((& $)) = a-d b + c d) V be the map Write down a basis for ^²(V), A³(V) and ^^(V) Find the matrix for ^³(T) : ^³(V) → ^³(V) (hint: it will be a 4×4 matrix) Find the determinant of T

I know the basis converted to orthogonal is {<2, 1, -1, 1>,<11, -12, 5, -5>,<-1, -3, 0, 5>} and that the magnitude of these will be sqrt(7), sqrt(315), sqrt(35) - but I'm not sure how to use these to convert the basis to orthonormal.

36. (a) What matrix transforms (1,0) into (2,5) and transforms (0, 1) to (1,3)? (b) What matrix transforms (2,5) to (1,0) and (1,3) to (0, 1)?

Find a basis for Row(A) and for Col(A). Row(A) Col(A) A = 9 4 -5 19 8 1 4 3 118 ↓ 1 0 OF}