In Exercises 1–2, find the rank and nullity of the matrix A byreducing it to row echelon form.2 -14-21. (a) A =-3348-44-23(b) A =| -3-1-458-21-1-3132. (a) A...

Extracted text: Q4) > In Exercises 1–2, find the rank and nullity of the matrix A by reducing it to row echelon form. 2 -1 4 -2 1. (a) A = -3 3 4 8 -4 4 -2 3 (b) A =| -3 -1 -4 5 8 -2 1 -1 -3 1 3 2. (a) A = -2 -1 -1 3 3 37 (b) A = | -3 -1 4 -2 1 -4 -2 Q5) > In Exercises 33–34, let u = (u1, U2, U3) and v= (V1, V2, Vz). Show that the expression does not define an inner product on R, and list all inner product axioms that fail to hold. 33. (u, v) = u¡v} + užuš + užu} 34. (u, v) = u į Vj – U2V2 + uUz Vz > In Exercises 35-36, suppose that u and v are vectors in an in- ner product space. Rewrite the given expression in terms of (u, v), |u', and ||v||². 35. (2v – 4u, u – 3v) 36. (Su + 6r, 4v -Зu)