1. Let B = 3 {B][F][C])}---E] and x = 3 -3 0 a. Show that both B is a bases for R² -8 3

Q: Suppose [v] is as follows. B₂ [V]B₁ [V]B₂] 2 = = 6 8 10 If ordered bases B₁ B₁ = {[7] [4]} and B₂ =…

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Q: Ixe A) e¯(1 − x) + C el-r 1-x B) -I dx = +C x C) -e (x + 1) + C D) −æe¯ª + C E) e(x + 1) + C

A: Topic = Integration

Q: а. v(Ã ·) = Ã × (V x B) + B x (v x Ä) + (Ã ·v)Ē + (B · V)Ā b. · (Ã × B) = B · (v × Ã) – Ã · (V × B)…

A: Part(a): ∇A⇀·B⇀=A⇀×∇×B⇀+B⇀×∇×A⇀+A⇀·∇B⇀+B⇀·∇A⇀ From the left-hand side of the given equation,…

Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

Q: X = { Ø₁ A₁ A², 3 and X₂ = { 0, B, B², √ ² are o fields but X, U X₂ is not. Why?

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Q: 2. Assign Hermit's interpokting tolynomial by The fallowingy da ta:

A: The Hermite's interpolation polynomial is H(x)=∑ui(x)⋅yi+∑vi(x)⋅yi'. Here…

Q: Let a, b, c and d be constants and define 1 a a² a³ 1 b b? b³ A = 1 1 d d d3 Without using cofactor…

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Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

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Q: Suppose ū = 2j + k, ū = 2i – 4j + 2k and w = -5i – j+ k. %3D Compute the following values:

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Q: 4). Use rules of replacement to prove the following: a). (p^~q) (p^q) = p b). (pvq) →→ r = (p → r) ^…

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Q: Does the following set of polynomials {t? + 1, t2 + t,t + 1} span P2?

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Q: 6.- Evaluate T(au + bữ), considering the following 1 T(ī) = 2, T(5) = , T(ī) 2, a = -1 and b = 2 3…

A: T(au+bv)=T(au)+T(bv)

Q: (x° – xº) (1+x³)5 Evaluate dr; Use B(m, n) = dr (1+x)m+n

A: Using the given result and

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

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Q: Use the column-viewpoint to compute the product C = AB of [1 A = 1 = 1² 91 0 -17 1 2 and B

A: Given matrices:- A=1-11102 ,  B=201-1

Q: Hiw.sLetAzi+j-2K,b=-i-k and c=zi+uj-zk,finds t Ax(B+C)- 3 CA-B)xC s-(AXB)ec 2- A (2B-c) 4-2Ax 3B 6-…

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Q: Prove BCスツ+)B[スかリック =B(X1y)

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Q: Evaluate: ₁²-du So -3 (x² y²)²7 x+y du dt

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Q: Which of the following statements are correct for the pde -2uxxx +3vxt-7u, = e sinx Auft A) Linear,…

A: This question  is about  partial  differential equation

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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Q: Q1) Write the following in scientific notation 1.) 1.234*10 2) -8.765*10402 3.) 1015

A: Given notation can be solved by formulaes

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

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Q: Prove that {4a + 126 : a, b E Z} = {4c: c € Z}.

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Q: In RX1, let U = span ( 1 Find bases for U- and (U-)+.

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Q: b) Use an algebraic proof to show that (AUB) - (AUC) = (B-C) - A

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Q: 2. Show that if 8=(AB)- then - > N - - (AB)² + (aß)² – (αB)² – (AB)² = [(A) − (α)] [(B) − (ß)] +…

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Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

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Q: 1) Name the polynomial a) 3x? + 9x - 1 b) 2x* - 9x? - 1

A: a) 3x2+9x-1The above polynomial has a degree 2⇒It is quadratic polynomial

Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: (b) f Gx) = 4x-236 A B Gx+i)Get 3 (2x+) Gett) GetB) 2x+) find AIBIC

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Q: 2. Compute each set of roots and provide the results in Cartesian form a) x5 = a = -1

A: As per our company guidelines, we can solve first question for you. If you want other question to be…