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1, U2, v3, U4E IR 1 = 2v2 = 3v3 = v 7. Determine if the set W = 4v4} is a vector space. If it is, find its dimension and a basis
3. If 3V1-2V2 + V3 w, and A is the matrix whose columns are V1, V2 and V3 and x is an unknown vector, determine whether each statement is ALWAYS SOMETIMES or NEVER true A. The equation Ax w is consistent. B. The equation Ax w is inconsistent. C. The equation Aw = x is consistent. D. The equation Aw =x is inconsistent.
(1) Prove that QV2+3) Q(V2, V3) (2) Prove that (Q(V2, v3):Q) 4 (3) Find the minimal polynomial of V2 + V/3 overQ.
all parts 3. (a) Find a basis for (Q(75) over Q. (b) Find a basis for Q(73, 77, 75) over Q(75). (c) What is (Q(V3, 77, 75): Q]?
find x. round your answer to the nearest tenth of a degree. ✓2 v3 ✓ 5 Find x. Round your answer to the nearest tenth of a degree. Check Type here to search
6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the point (A) v3 (E) 2v3 (B) 1+2V2 (C) 2 v3 (G) 3/2 (D) V2 6. Consider the sphere S cut out by z2 + y2 22. Maximize (Daf)P where y, z) 2y +3z and u is a unit vector in the tangent plane to S at the...
Q 3) Find v1, V2 and v3. + 30 V – + 20 V – - 50 V + + v2- 40 V
Let E = F(a) be a (simple) extension of F. wherea E E is algebraic over F. Suppose the degree of α over F is n Then every β E E can be expressed uniquely in the form β-bo-b10 + +b-1a-1 for some bi F. (a) Show every element can be written as f (a) for some polynomial f(x) E F (b) Let m(x) be the minimal polynomial of α over F. Write m(x) r" +an-11n-1+--+ n_1α α0. Use this...
Problem 3: Determine the splitting field of the polynomial (2 -2)(2-3)(2 -4) over Q. Find its degree over Q. Verify if all points of the splitting field are constructible. Problem 3: Determine the splitting field of the polynomial (2 -2)(2-3)(2 -4) over Q. Find its degree over Q. Verify if all points of the splitting field are constructible.
Problem 1 Find the limits of the following sequences (i) an- {V2, V2V2, \V2V/2V2, (iiu )