Let a = (1,2, 3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) =2(a · b) + (a · c).

Q: If (a,} and {b} divergent then {an + b,} is divergent. are True False

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Q: Show that [x, p;] = iħ.

A: note :  As per our company guidelines we are supposed to answer ?️only one question. Kindly repost…

Q: Express the following: as a linear combination of u = (2, 1, 4), v = (1, -1, 6) and w = (2, 2, 8).…

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y+ z + w= 6 .…

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Q: Let u, EC prove that ū · v = v · ū น

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Q: If {an} and {bn} are divergent, then {anbn} is divergent.

A: Given; (an) and (bn) are divergent.

Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: a+ib a) If x+ iy = prove that x? + y² = 1. a-ib

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Q: verify that (A + B)T = AT + BT

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Q: Prove that c = cn. i=1

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Q: Show and use d(Xn, FCN))<« d(Xn-1 'x) Vny? To prove X = fx) %3D

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Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express z x and zy in terms of fu , f y, and the…

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Q: Prove Theorem| 2.3: (i) (A+ B)" = A" + B", (i) (A")" = A, (iii) (kA)" = kA".

A: To prove the given transformations

Q: ez = -2

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Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

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Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: Let A = {-i, .,-2, –1,0,1, 2, . i}. Compute the following a) U는1Ai A? = {?} A? = {?}

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Q: If Σa, is divergent and Eb, is divergent, then Z(a + b) is divergent.

A: The given statement is false as sum of two divergent series may converge. We illustrate this as…

Q: prove that T= S.

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. 5 x + y + z + W = -7 5x + 3y - z +…

A: Here we have to use cramer rule for solving the system of linear equations

Q: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

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Q: prove that 2,

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Q: Express E: livenr coumbination of Ÿ; = and V as a

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Q: Find (a) ATA and (b) AAT. Show that each of these products is symmetric.

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Q: F(p), then prove that

A: simple use of integral transformation

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: Let ū = 2i – k and ī = i+3j + k. Compute |ū], |T], ū x ī, and Projzū.

A: Solution is here

Q: Prove Theorem  A + (B + C ) = (A + B ) + C .

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Q: а. Complete the basis step of the proof.

A: To prove that:              ∑i=0n2i=2n+1-1  for any nonnegative integer n.

Q: See picture

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Q: If (an) and {b,n) are divergent then (a, + b,) is divergent. a) true

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Q: Let 1 1 1 1 2 3 3 A = 0. 1 -1 B = 2 2k -6 1 and = 4 %3D -1 1 3 5 4k 11 Solve Az = b using Cramer's…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dr is divergent a true b) false

A: We have to calculate  ∫1∞1x2 dx.

Q: 2. Jui (x) + Juo, (x) = 2Y Jv (X) 2. Jv-iCX) Juo, (X) Jv(x)

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Q: dv Prove that 4u/2n

A: We use Gamma function to prove the given result.

Q: Prove that −(−v) =v

A: To prove: --v=v

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: ion Prove that for

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Q: Prove that where e, > (1,0)"

A: Prove that     conve1, e2, -e1, -e2=x∈ℝ2 : x1+x2≤1 where e1=1, 0T , e2=0, 1T.

Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

Q: Let a = (– 1, 5, 0) and b = (3,0, – 1). Find the component of b onto a.

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Q: -x+y<y. 2 If x < y, prove that x <

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Q: Q1. Prove that KT = = -.

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Q: 2} and {bn} are divergent then {an + bn} is divergent.

A: Given that: an and bn are divergent.

Q: (a) Verify the Cayley-Hamilton theorem. (b)  Use the theorem to express A2 and A3 as linear…

A: Part (a), Let, A=4-112 Now, the characteristic equation of A,…

Q: z, Z2 Prove

A: If z =x+ iy then  z = x- iy. i2 =-1.

Q: Prove that Srxdr = 2[, , da, r × dr =

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.