B. Let a =3 -2 1], Find a value for k so that the dot product of a with b=[k 1 4] is zero.

Q: 5. Determine given: axty - bxy = 36 %3D where a and b are constants.

A:

Q: In real-number multiplication, if uv = uw and u # 0, we can cancel u and conclude that v = w. Does…

A: To explain: either v=w or give counter example.

Q: В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

A:

Q: show that }I f,lm) Ck-m) 2.

A: For, ∑m=0kf1mf2k-m, substitute k-m=n or m=k-n: ∑m=0kf1mf2k-m=∑k-n=0kf1k-nf2k-k-n…

Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: Find the Ker(T) and Rng(T) and their dimensions. T:R → R defined by T(x)= Ax , where 1 -1 A = -3 3…

A:

Q: In ABCD, H is the centroid. If HF=6 find BF. C E

A: It is known that the centroid of a triangle divides the median in 2:1 ratio. It is given that HF=6.…

Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

A:

Q: Show that under the transformation: k= the equally spaced z-values, z : 1o, To +h, xo +2h, .…

A: Just substitute the given values of x and proof will follow.

Q: Say that E = Ãek™, where the components of A and k are real and constant, i.e. they aren't imaginary…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: . For j = 1,..., N, let Ij = [aj, b;] with a; < bj, and let I:= I1 x -… ·x In. Determine a1. (Hint:…

A:

Q: (c) Prove that 1, have equal roots if e= a'm +b °

A:

Q: Give the condition which ensure that Je-| < 1 where z E C.

A:

Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: Let x = 21 +mj and ỹ = -3ī +8j. Determine the value of m if: a) x and ỹ are collinear b) x and ỹ are…

A: Answer: a) x→ = 2i→+mj→ and y→ = -3i→+8j→ are colinear if m=-316 b) x→ = 2i→+mj→ and y→ = -3i→+8j→…

Q: In AAEC, G is the centroid. 6. D 世 B If EG = 6, find GB. O 2 O 3 O 6

A: Centroid of a triangle is the point of intersection of the medians of the triangle.  Centroid…

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

A:

Q: Given that n ≥ 2 , x ∈ Rn  Prove that there exists a y ∈ Rn in where y ≠ 0, and xy = 0

A:

Q: Show that the finite difference formula 1 Dzu(î) = [Зи (т) — 4u(г — h) + u(т — 2h)] 2h is a…

A:

Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: 1 1 dr = In a. find the exact value of a. %3D V16+9x? 19+4x*

A: Here we will solve for 'a' step by step answer given below,

Q: for z = In(2® + y*). Find

A:

Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

A:

Q: () Let z = x + iy. Find Im and Im 2 in terms of x and y. Im Im z2 ||

A:

Q: Find values a, b, c, d such that the function (x+ 1)³, -2 < r <-1 s(x) = { ar³ + bæ² + cx + d, -1 <…

A:

Q: Let x, y E Rn be given. (a) If ||x|| = ||y|| = 1 and x y = 1, show that x = y. (b) If ||x|| ≤ 1 and…

A:

Q: Suppose AE R, v#0, and (A- A)v#0. Use the fact that A is symmetric show that it is impossible to…

A:

Q: Given: 5x+4y= 24, x + 7y= 11; Prove: y = 1

A:

Q: Consider P2 with the inner product given by evaluation at - 2, 0, and 2. Compute ||p|| and ||q|| for…

A:

Q: Let a,b E R with a # 0, b # 0. Prove that (ab)¯1 = a°1b´1. %3D

A:

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: Consider the figure below. Assume that 41p,1, 1q, m263(5x+4)° m28 = (10x – 19)° a. Determine the…

A: straight line angle is 180 so ∠4 + ∠3 = 180°  if two lines are parallel then alternative interior…

Q: Given: A e M2x2(R). a. Given T: M2x2 (R) → M2x2 (R) as T(M) = AM, prove that rank (T) = 2rank(A). b.…

A:

Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

A:

Q: In real-number multiplication, if uy1 = uy2 and u ≠ 0, we can cancel the u and conclude that y1 = y2…

A: Given:

Q: If z = x – 3y, then w = 2 Using the calculation above, mark the s

A: Linear span: Let V represent a vector space, and S=v1,v2,...,vn represent a subset of V. If every…

Q: Let →a=⟨7,−5⟩ and b→=⟨1,3⟩. Compute the dot product. →a X →b=

A: Given a→ = 7,-5 and b→ = 1, 3. We have to compute the dot product a→·b→.

Q: 10 Consider A :3D and y:= Find all re R that minimize || Ar - y|l2.

A:

Q: Given the function z = In (2xy + e3x) - 5y, %3D az a. ax

A: Since, we have to find the partial derivatives ∂z∂x and ∂z∂y of functiongiven by z=ln…

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: a- If A = -1 %3D 2 and B = -41 prove that (A + B)T = AT + B". 12 [1/2 - If A-1 =1/2 -1/2) and |A| =…

A:

Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

A:

Q: For the missing elements to satisfy the condition A-1 + 14 = E %3D 1 e b 3 -2 -3 A = 4 -2 i Ly a 268…

A:

Q: Find conditions on a, b, c, and d such that

A: Find conditions on a, b, c, and d such that  B=abcd commutes with both 1000 and 0001 For any matrix…

Q: 2. find the the following equation in simplest arbi Saution set of form. X-3x + 9 = 5Y-10

A:

Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

A:

Q: 2- Calculate the part a) using the given countour and assuming that R → o. For part b), e 3ix use…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: D B. E C Given: AB XEB = CB × DB Prove: AABC- ADBE

A: To Determine: prove △ABC~△DBE Given: we have a figure in which we have triangles △ABC and △DBE also…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.