4. Let U = {(a,b, c) |b = 0} and W = {(a,b, c) | a +c = 0}. Determine whether R³ = U + V. If so, is the sum direct? Why?

Q: snip

A: Given points : P1= (3,-4)  and P2 = (-2,1)

Q: 4. Show that for all formulas p, ý, 0 € S(P), (a) (y = ) = ¬(e^ ¬b).

A:

Q: Suppose that X, Y C U. If Pr(X) = 0.3, Pr(Y) = 0.32, and Pr(X n Y) = 0.08, what is Pr(X' U Y)?

A: Given :  X , Y ⊆ U . P (X) = 0.3 , P (Y) = 0.32  and P(X∩Y) = 0.08 .  To find : P (X' ∪ Y) = ?   The…

Q: 11. If AMNP is reflected across the line y = 2, then translated using the rule (x + y) – (x – 8, y –…

A: given,

Q: (d) Illustrate the other De Morgan's law by selecting the region(s) corresponding to (A N B)° on one…

A: De Morgan's laws are a pair of transformation rules that are both valid rules of inference.

Q: 8. If s is t less than four times u, what is t in terms of s and u ? F. 4u + s oG. 4u- s H. u+s J. U…

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Q: Prove VZEC, V2|z|>|Re z| +|Im z| + |Im z| Vze C,

A:

Q: 4. What are the values of A, B, C, and D so that 1 a. A = b. A = C. A = d. A = HALA00 B= C= B B 1 8'…

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Q: 4. Write a flow proof, Use the information from the diagram to prove that A ABD A CDB. A ....

A: Given:

Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

A:

Q: 20. Let (). ()- u = v = If æu + yv = w. (æ, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2 (D) –1/2…

A: To find the value of x-y from the given vectors.

Q: If →               →       v = (x, y), || v || = 4, and →           w = (−2x, −2y), then →…

A:

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

A:

Q: Suppose V(x,y) = (2x, 2y) and W(x,y) = (x,y + 3). Is V o W = W o V? Justify your answer.

A:

Q: 3. If z=2cis TT/6, what does z^6 equal?

A:

Q: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

Q: What is the normal line to the line that passes through (-8 , 0) and (-1, 3) 3x-7y = - 24 O (x/8) +…

A:

Q: Is S = {a + b√(2) : a, b ∈ ℤ} dense in ℝ?

A:

Q: Q.8 If v = (x² + y² + z?)¯/2, prove that a2v + ду? = 0. ax2 az2

A: We find second  the partial derivatives lf given function with respect to x, y and z and then add to…

Q: 5. Prove that if x, y ER, then x + y ≤ x + y. Use the following cases: (i.) x, y ≥ 0, (ii.) x, y <…

A: We now prove that if x,y ∈ ℝ , then x+ y≤ x+y with the help of given three cases.

Q: 43 If uzzt+y+z , u?v =y+z,u³w=z, Show that a (x,4,z)

A: Q3. Here, u=x+y+zand,u2v=y+z⇒v=y+zu2=y+z(x+y+z)2and,u3w=z⇒w=zu3=z(x+y+z)3

Q: too x(Ju) - xt) e ot * the famer heansfarm ナR X( Jw) Sen %3D

A: Fourier transformation of a function x(t) will be X(t) and inverse Fourier transformation of…

Q: -27 -36 81 onstruct it in R. 37, 65, 0,

A: * Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at…

Q: Q2: Suppose A = (0,2,4,6,8), B (1,3,5,7) and C (2,8,4). Find 1) AUB %3D 2) Ance 3) BnC 4) C\B

A: Given, A={0,2,4,6,8}, B={1,3,5,7} and C={2,8,4} To find, 1) A∪B 2) A∩Cc 3) B∪C 4) C\B

Q: Q1 find acubie palonemiat ofk given-points for27,3},(2,12)e

A:

Q: Proof by contrapositive that for x, y ∈ Z, if xy is even then either x or y is even.

A:

Q: 9. Using the fact that ||u|| = 2, ||v|| = 3, and u x v = (-1,5, 1), find u · v.

A: You have asked multiple  questions and not mentioned  which questions answered you need , so…

Q: What is the sum of P(x) and Q(x) if P(x) = 4x2 + 6x - 9 and Q(x) = -7x- 12x +8? %3D 1. -3x2 - 18x -…

A: Given P(x) = 4x2 + 6x – 9 d(x) = -7x2 – 12x +8

Q: Prove: For allintegers aandb, if a|b then a² |b²

A:

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: p(x, y) 3/24 2/24 1/24 1 2/24 5/24 2/24 2 6/24 1/24 2/24 Е(X), Е(Y), H(X), н(Y, НХ Ү), аnd HIX, Y)

A: It is an important part of statistics. It is widely used. Since the question has multiple sub parts…

Q: In R4, let S = span{(1, 1, 1, 1)T ,(1, 2, 1, 3)T }. Find S⊥.

A:

Q: gla): [veri de, fued g'la). ☺ Compute #4.@ If ) es ds -6

A: if function is continuous on interval [a,b], and  Above rule is also called Leibnitz rule of…

Q: Find the Duf of S(x,y,z) = 3xvy+4xz² from Po(2,1,1) to P(4,7,2) %3D

A:

Q: a) By using the substitution u = √√x +3, evaluate S. 2 √(√₁ + 3)2 d. dr.

A: Given, ∫142xx+32dx

Q: Q2: Suppose A = (0,2,4,6,8), B = (1,3,5,7) and C= (2,8,4). Find 1) AUB %3D 2) Ance 3) Bnc 4) C\B

A: Given A = 0 , 2 , 4 , 6 , 8B = {1 , 3 , 5 , 7}C = {2 , 8 , 4} then (1) A∪B = {x : x∈A or x∈B}= {0 ,…

Q: Prove using INDIRECT PROOF: 1) P → Q 2) R → S 3) ﬢQ ۷ ﬢS ﬢP ۷ ﬢR

A: The statements given are as follows: P→QR→S~Q∨~S For the first statement, we will apply the…

Q: 8 - If w = is a linear combination of v = and u = then r and s must be, respectively,

A: w is the linear combination of u and v then we can write  w= au + bv  Where a and b is the scalar

Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: When is it true that u+v= v+u?

A: Answer: It is true when is commutative property.

Q: (: :)-- (;) (:) -- (") a ven if the complete d 2 lution to this system is r = nere a is any real…

A:

Q: (b) Using Venn Diagram to prove that (A U B)e = A° N B° ?

A: To prove the following using Venn diagram A∪Bc=Ac∩Bc First consider the left hand side  Set A

Q: Q1) Compute the products using the definition as a linear combination. 8 3 -4 1 2 1 5 1

A: As per the definition of linear combination abcdef.x1x2x3=x1.ad+x2.be+x3.cf

Q: Let z, w e C. Show that |2 + w? + |z – w? = 2(|2|2 + |w?). %3D

A: We will show the given result.

Q: State the postulate or theorem that justifies the statement. 1/2 3/4 7. 23 = L7 8. 23 = L6 5/6 7/8…

A:

Q: uppose that X~N(µ, o²) and that P(X 3.6) = 0.6554, what are the alues of u and o?

A:

Q: When u × v = 0 and u ∙ v = 0, what can you conclude about u and v?

A:

Q: Let z, w E C. Show that |z + w[? + |z – w|? = 2(\z|² + |w|?).

A: Any complex number, Z can be represented as Z=x+iy, where x=Re(Z) , y=Im(Z) . The expression, Z can…

Q: a,b,x,y, are negative numbers a⁵ + b⁵<= 1 x⁵ + y⁵ <= 1 prove that a²x³ + b²y³ <= 1

A: Given information: The numbers a,b,x and y are negative numbers. The conditions are a5+b5≤1,…