17. In R² (column vectors) show that (x, y) = x² Ay is an inner product where 3 A = ¹- (³7) -- (-)). - (1) = . y = 1 X2 What is the corresponding norm ||™||?

Q: Let x₁ = a +bt² +c+z₁, t=0, 1, 3,... where a,b and c constants and z, ~WN (0,0²). a) Let U₁ = x,…

A: Given, xt=a+bt2+c+zt , t=0, 1, 3, . . . where a, b and c constants and zt~WN0, σz2.

Q: 1. The vector X = k is a solution of x - (: -)x-G) 8, X' 2 for k = Enter only the value of k.

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Q: 2. Let a, B, y be three vectors in the inner product space V½ (R) with the standard inner product…

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Q: Find the branching points of the given complex functions a) f(z) = vz+ vz– 1 b) f(z) = vz² +9

A: A branch point of an analytic function is a point in the complex plane whose complex argument can be…

Q: Vector fields V and W are defined by V- (2х — Зу + z, -3х — у + 4z,4y + z) W- (2x - 4y — 5z, - 4x +…

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Q: Lw(s) ~ 1 – Show that 1 is MTTF where

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Q: v : {p, q, r, s, t, u} formula (t → g)A (u → p) A (T → s) ^ (tAg → r)A (s t)^ (uAp + 1L) Find an…

A: Given that v:{p,q,r,s,t,u} to {0,1} It satisfies a formula, (t→q)∧(u→p)∧(T→s)∧(t∧q→r)∧(s→t)∧(u∧p→⊥)

Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: Compute the orthogonal projection of onto 7. Use the square root symbol 'V' where needed to give an…

A: Given u→ = -996,  v→ = 1-1-1

Q: ...,N, becomes Y = a, + a,X. Q6. (a) If the least square line of points (xţ, Y1), i = 1,2, ... ..…

A: We are given the following equation To calculate the slope parameter a1  the formula is To…

Q: 2. Prove: a. [(x)b~ XE]~ = (x)b XA b. Эх (~p(x) A ~q(x)) = ~[Vx(p(x) V q(x))] 3 Dariva

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Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

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Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

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Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

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Q: 3 0 -2 3-Let A= 0 1 2, B= Find:- 3 L-1 1 5] (2A – I)B' and show that (BA)'=A'B'

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Q: 2. Use abbreviated index notation to prove or disprove the following statements involving arbitrary…

A: Since there are multipart, so here find the solutions of first and second part.

Q: Find r'(t), r"(t), r(t) r"(t), and r(t) x r"(t). r(t) = 32²1 - 4tj + 12³k (a) r(t) (b) r"(t) (c)…

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Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

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Q: Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of…

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Q: 5. For a = 3i-j+2k, b=2i+j-k and c=i-2j+2k, find (a)(a^b)^c and (b) a^(b^c). Comment on the need for…

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Q: By substituion, u=(y/x) in equation xy'=(x2+y2)1/2 we have u'*x+u=(?)1/2. a) u b) u2 c) 1 d) u3…

A: Substitution in differential equation

Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: • The Doman of f(x) = 4 – Vx is 1. (2, 0) 2. [-2,0) 3. [2, 00) 4. [-2,2]

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Q: (Q1)-A-State(First fundamental theorem) and Show that :(2₂0 /(10), +..) -B-Let f:( M, (Z).+-)-(M,…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: 5. (10pts) Let A be a positive definite nxn matrix. For any x = R", let ||X||A = √(Ax, x). Show that…

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: 10. Given R = x7 + y3+ zR, and r = |R show that (a) V x (7 x R) =7 + 7R, (b) (A x V) × R = -27, (c)…

A: Given: be any constant vector.

Q: 2 3 ). (: :) Let mį = m2 = m3 = 2 Determine s if n = 4 3 E Span(my, m2, тз).

A: For the given matrices m1 , m2 , m3 and n and using the statement that n lies in Span ( m1 , m2 , m3…

Q: 6. Suppose that u₁ and u₂ are vectors with ||u₁||| = 2 and ||u₂|| = 3. You are also given that u₁ ·…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…

Q: Let Compute дw -(-2,-2) = -(-2,-2) = მs дw St W = 2xy - 2yz + 3xz, x = st, y = est, z = t² =

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Q: 660. Let A = (1, 5), B = (3, 1), C = (5, 4), A' = (5,9), B' = (11, –3), and C' = (17, 6). %3D Show…

A: according to the problem, we have

Q: 9. (a) are perpendicular to each other. Determine the algebraic condition such that the vectors č=…

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Q: 6) Find solution of the particular y"-2y'+y=x²-6x+ 2x

A: 6)Here the given differential equation is y''-2y'+y=x2-6x+2xe2exlet y=emx be the trial…